I'm going to DM a campaign in a while, and I want to know how do I get the players to get in character at the beginning of their story. I want them to get comfortable with their characters and RP with each other. Our current DM with the same group isn't great unfortunately. He is extremely non-descriptive when DMing (eg. He will say: "You arrive at a town" Instead of describing it), and the only preparation he does is a vague idea of what will happen. It used to be better but he's been putting noticeably less effort in and is planning to end the campaign rather prematurely. The players and himself are getting bored, and I just don't want my campaign to end up like his. 

So, how can I get the players to RP and form group dynamics, and make the campaign feel alive?

First thing I would say is not to expect too much too soon. Most characters evolve over time and, at the start people need to take time to get a feel for who they think they are. 

The best thing you can do to help them decide is to give them choices. Making choices in characters is a great way to discover them, especially in instances where their choice and their players' differ. 

They don't even all have to be choices of earth-shattering proportions. When I'm starting a campaign in a tavern for instance, I'll usually start by asking players what their characters order (food or drink), and even that small prompt can plant some interesting seeds in players' minds. 

Something I've noticed could help is a short pre campaign session. I've always found it easier to fit into character when I'm isolated, or just less busy with other characters. A few hours to introduce the begining of the game with a few choices and minor encounters to get them a taste for the story and their own characters. When you give a player more attention, and an opportunity to talk more, they tend to be more willing to explore. However, the begining is always the hardest part to roleplay. So just keep up with giving the players something to do and feel, and they'll hopefully feel themselves out.

I started them in a city together the day before Spring begins.  They were going to receive their adventurer's credentials in the morning, so many (N)PCs would gather that day.  Then I just gave them a reason to stop in at the tavern and gave them an invitation to introduce themselves.  You can lead a horse to water, but you can't make them drink.  They will do as much or as little as they think the situation needs.  You usually don't get real ambitious role players in a casual game.  But if you do, dish out the DM inspiration.

As others have said, you can't just "make" your players roleplay. You can only provide opportunities like bait for them to take if they want it. Have NPCs ask questions, put pieces of the world in front of them to interact with, and when all else fails just straight-up say, "What does Grognoramus think of that?"

You're not going to get them to hold long, spontaneous conversations in funny voices right away. Just aim to get them into their character's heads. Make sure they filled out bonds/flaws/etc and call them out sometimes when those might come into play. In my experience once they get over the initial hump they have a persona built in their minds and they pick it up and run with it.

In terms of making the campaign feel alive, that's just work. Like you said, your current DM isn't putting in the work and it shows. Players can't have enthusiasm for your world if you don't have it.

This is what I'm doing for my upcoming game. I'm running three 'Preludes' that focus on the three pillars of play (combat, exploration, social interactions) and showing the general story of the setting and adventure hooks by having players run NPC characters on a quick adventure. The results of their choices as the NPC's will feed into the session zero information for the acutal player characters enabling the players themselves to use what they learned about the wider world as an NPC to make a character with that greater world understanding.

I suppose the tl;dr is: Give them information in fun ways so they aren't making a character in a void of ignorance about your setting.

Talk with each player, and have them write out on cards things that the other characters might have heard about them, something like 3 positive true things, 1 negative true thing, and one false rumor, then when you start, you disperse the cards for each of the characters to the other characters, so everyone knows some things about the others, mostly true, but they have no way of knowing which parts might not be.  This gives the players something for their characters to talk about, kick-starting roleplay.

Also if you make sure they have at least a general idea of the setting, and talk to each of them about where their characters are from, and what their upbringing was like.  If they don't already have a backstory idea when they build the character, use their features such as Background to get things started (Two characters with the same race and class will have extremely different backstories if one's an Urchin and the other's an Outlander)