So as a DM, I've only had real success by homebrewing adventures and settings. However, I really like the Prewritten adventures and would like to give them a serious try! I have attempted running from the books before but I always run into the same problem and its led me to thinking "Am I doing this right?".

Each time I have tried running from a book it always feels like this:
DM: "You see X, Y, and Z. What do you do?"
Player: "I go to X."
DM: "Hold on...." *Flips through book and skims section talking about X. Taking up too much time "Ok, so blah blah blah..."

Player: "Now I go to Y."

DM: "Hold on..." *keeps flipping through book notices. that if X was done before Y, then X should have been done differently. "Actually scratch that, it actually happened like..."


And so on and so forth. 
Am I supposed to have basically memorized the book? or do most people deviate from whats written completely?
In my Homebrew games (which I am infinitely better at) when the party does something, I just make stuff up CONSTANTLY and worry about implications later lol

I've never run one of the large adventure books, as I have little interest in them and I suspect I'd have the same problem you're describing. But, I will say, I do quite enjoy running small published modules. 

I have Tales from the Yawning Portal and Candlekeep Mysteries, and they are nice and fun to run. They're specially nice to use in my sandbox campaign since, as modular adventures, I can pepper them into the world to broaden the players playing field without having to do all the work myself. 

I'm currently also running Dungeon of the Mad Mage which, while anything but small, is very straightforward as a Dungeon crawl, and my group (who normally leans towards more narrative- focused  games) are finding it a nice change of pace. 

My only main piece of advice for running published adventures is to read ahead on your free time. You don't need to read the whole thing before you start it or anything, but just flip through and familiarize yourself with some major points, see where your players are and try to trace a few paths through the adventure you think they might take from there, and in general try to read at least a session's worth of content ahead. It also pays to read the end first, in case it has important info on the main story/ main bad guy's plans. They should really publish that at the beginning. 

I think even with modules you need to be ready to improvise when it feels appropriate. Personally I feel a lot more comfortable reading through the whole thing ahead of time so I can better understand the consequences of the players' actions and can still see the end goal the modules is aiming at.

I heavily homebrew any Adventure book I run. Whether it's swapping out characters I find boring with someone I find more interesting, or adding in my own side quests to the story... I do think it's smart to read the entire adventure at least once before playing... if you're only reading as you go you might not realize that a minor detail in an earlier chapter has a callback later. But don't be afraid to just homebrew it... if players do something and you want to just say, "Okay, this thing happens" and you just make something up and you read ahead and realize it creates a contradiction... just change what it means. This is also a big help if you're playing with experienced players who may have played through this adventure before, since it makes it feel fresh and exciting for them.

I was exclusively a home brew dm for about 30 years. Last year I decided to pick up 5e and start running adventures from it, starting with Rime of the Frostmaiden, and then moving into Curse of Strahd.

My players and I had a blast, we played every weekend for a year without interruptions, except for the occasional birthday, significant event and all. 

I used to have nothing but contempt for the DMs who ran “store bought” adventures. After I ran one I figured something out, those “store bought” adventures are just like the pirate code, more guidelines really. I also found out that even with a premade adventure, pretty much the same stuff happens in a home brew. 

The players go to new, exotic, and exciting locations, meet interesting, and exciting people, and kill them in horrible and creative ways. The basic principles of DnD being investigation, detection, conflict, and a resolution, those are pretty much hardwired into any adventure, home brewed or premade. 

The only real question is which do you prefer to run? Prep time can absolutely get you out of that flipping-through-the-book bit and help it all flow better.

Either way, do what you enjoy, I like mixing in my own style in premades now, it keeps me from having to draw maps and crap out npc stats for a guy the party kills in two hits or buys 2 weeks rations from and never sees again.

There is a great interview with Matt Mercer where he and the DM interviewing him talk about how they just don't really like modules, or if they run them they usually end of home brewing them and changing them and I can appreciate this. 

I find Modules need much more prep then a Homebrew, with a homebrew it is all in my head because I have created the skeleton and so I can tweak and react on the fly far easier. With a pre written module I tend to disect the book at the start, create flow diagrams so I have a really clear diagram of the things that can happen, the things that are important and the things that are side quests. I usually make copies of all the maps, or draw them by hand, or find them online or make them online so I have easy to grab versions, I just put far more work in making the contents of that book usable behind my screen to the point I really rarely actually reference the book directly in session at all. 

Running the modules exactly as written isn't wrong, but neither is doing your own twists and turns. Actually, many of the adventures are designed for you to insert your own sidequests and adventures into them. There are literally sections of like... Dragonheist, where the book is like "and now the characters independently adventure until level 3."

Honestly, here is my tip for running a hardcover adventure: read through and familiarise yourself with the next few games of content. And any characters that don't catch your interest or attention, change them until they do. While running Dragonheist, there is Renear Neverember, who is a harper and a noble and blah blah blah, he's a grey smudge of a human being. Completely uninteresting. I was having real troubles getting inside his head. And just one day walking to work, I just started doing a Matt Berry impersonation. And that's how Renear became one of the stand-out most compelling characters from that campaign for my players. He was undoubtably a good guy, but he was the sort of person to tell a commoner to sacrifice himself because he, as a noble and a warrior, was more useful to the side of good. And if you are familiar with Matt Berry's theatrical, over-the-top voice, then imagine the scene where my players were coming back from the Opera, and Renear meets them in the alley in front of their Bar and quiet loudly and dramatically declare "As you well know, I am a harper!" Which was a laspe of me forgetting the Harpers were a secret society but was just the perfect encapsulation of that character. And Matt Berry Renear isn't in any book. No one told me to include him.

Use the hardcovers as a guide, but make them your own. If you don't understand why something is in the book, then change it. Because the books aren't one-size-fits-all. There are parts that will work with your style and there are parts that won't and if you don't correct for that then your players aren't getting your best game. Because at the end of the day, whether you are running homebrew or a published adventure, the fact is that it is your game. In this regard, the only right way to run it, is the way that you and your players enjoy. If you only enjoy a dungeon from a book, then you can just use that dungeon. Or if you want to change the plot considerably, then you are free to do so.

I just wanted to comment that I had also given a character a Matt Berry impersonation, although for me it was Glasstaff from Lost mines of Phandelver. But I liked him so much I found an excuse to insert him into Hoard of the Dragon Queen.

Quote from LeBattery >>

In my Homebrew games (which I am infinitely better at) when the party does something, I just make stuff up CONSTANTLY and worry about implications later lol

I have just created a post to share my experience which is exactly as you said! (Droop is now a PC in my campaign thread). I have only run one prewritten adventure, LMOP, and have started flying by the seat of my pants since then, and have to agree that I found it much easier to do exactly as you say. I'll drop in a situation, and sometimes the players read into something that just isn't there but I run with it, and let the players just do whatever to conclude it. Usually they come up with way more imaginative theories than I could have thought up, so I encourage them along and practically let them write it!

But even with LMOP which is a comparatively short module, I've run a couple of quests from Ghosts of Saltmarsh and DOIP too, and I do constantly flick through pausing the gameplay, and I felt that I was running it too scripted. I haven't yet got to the point where I can improvise in someone else's adventure. When I did attempt it once in LMOP, I messed up a pretty major plot point later, so had to modify the story!

I've probably spent equal time playing in homebrewed games as I have in published adventures, and I'd say they're about the same amount of work as each other. It's just a different type of work. I do try to run the published books as close to how they're written as possible, but it's quite clear that the authors understand and encourage you to change things to suit your group. You're going to have to improvise a lot regardless, and I think the longer you spend running these books the more comfortable you'll be in just making stuff up on the spot instead of flipping between the pages.

Like everyone will tell you, you absolutely do not need to read a book cover to cover before running it. It's much more like laying out the tracks while the train slowly rolls forward. Just keep a little ahead of your group, and what is likely to come up for them will be fresh in your mind.

Mix and match modules with your homebrew for best effect.  I typically take modules and then adjust them to my home world.  I'm currently running Keep on the Borderlands updated to 5E, with a full monster economy for the caves and three of the surrounding areas fully built out, some based on the original keep on the borderlands, another OSR module I've adapted and I've got an opening to move onto another adventuring area.  All told, its a large sandbox area that will take the players to level 5 and from there they can move on to other areas.  Essentially its a chapter one of a three chapter campaign.

You will become a much better adventure creator by reading other designers work and pick up techniques from them that you can apply to your own, from organizing to presenting information quickly.  Just go through some old Dungeon Magazine adventures and you'll see a lot of creativity that frankly WotC does not possess anymore.  I put in "Old Man Katan and the Mushroom Band" from Dungeon Magazine 41 into my sandbox and its a god damn masterpiece compared to anything WotC put out for 5E.  Tons of humor, good use of the campestri to comedic effect and a it works well to flesh out the Fell Fens.  Its even got Swamp Thing in there if the players decide to go that way with the creature.  All of that is from Dungeon.  There are also incredibly good 3rd party OSR content as well.  Try Dark Wizard Games "Moving Maze of the Mad Master" if you want a dungeon with a cool gimmick to baffle the players. 

The thing is if you only run your own content, and especially if you only use WotC 5E content, well you'll more than likely stunt your development mentally.  Look to some older content from D&D and OSR content and you'll be amazed at how well thought out and fun non-WotC content is.

Quote from TransmorpherDDS >>

I just wanted to comment that I had also given a character a Matt Berry impersonation, although for me it was Glasstaff from Lost mines of Phandelver. But I liked him so much I found an excuse to insert him into Hoard of the Dragon Queen.

 See, for me Glasstaff was Stephen Fry.

The fundamental problem with a module is that it has to be made one size fits all -- if the PCs do something unexpected, the module can't cope, so either a module will be super railroady or it will require the DM to do a lot of homebrew anyway.

The advantage of a module, however, is that there are a lot of background details (maps, businesses, minor NPCs, etc) that are a lot of work for the DM but not actually that specific to the characters. As such, I like using a module as a framework for homebrew storylines.

Modules just fundamentally require a lot more preparation if you want to run them as written. You may not need to memorize it but you do need to know where to find anything that comes up. Usually, characters work through things room by room and that is typically how a module is written. However, if the DM is just reading the content as it is being played then it will run much slower than necessary and is much less likely to give a fluid experience.

The best way to run a module is to read through the sections the players are likely to reach in the current session. Make some notes to summarize how the plot is supposed to go. If there are important things the characters need to do or other actions that they need to avoid or which will have significant consequences then make note of them. After that, the DM can read the descriptions from the text as the players enter the rooms and embellish as needed.

In addition, if the DM has a good idea of the intent of the module then there is no problem in adding/moving/adjusting/ad libbing content if it makes for a smoother or more fun experience.