While our heroes have amassed their “treasure” they are eager to exchange it for gold and/or buy magic items.   When your party is rewarded (finding treasure or given after a quest, etc) with items such as gems, art work, furs, and other related items how do you handle the selling to gain gold or other items?  For example your party has 10 gems worth 25gp each, a gold statuette worth 500gp, and an exotic fur robe worth 250gp (fill in other items) and they want to exchange these for gold or other items, what interesting ways do you create for an exchange?  

Do they have to adventure to a merchant shop in a larger city to sell the fur?  Do you allow common items such as gems easy trade at outlander settlements or exchanged for gold?  Do you typically make the exchange a nonevent or make it more interesting (or a combination or both)?

Honestly I don't put too much effort into it because shopping is less fun than other adventuring activities. Gems can be traded just like other currency. It helps players manage coin weight that way as well (gems are a lot lighter). Other treasures can be easily traded in most places, but some items (like a gold statuette worth 500g or art work) might have to be traded in a larger city. If I want to have a cool story hook, then I'll come up with an exotic item that they have to find a special dealer that leads to some other encounter. If the players have a home base, they sometimes just keep the treasures to decorate their home. 

This is going to sound stupid, but ... I don't. I hand out loot in various ways to make it interesting, but the minute it's transferred into the PC's inventory, I just consider it gold. 

There are a few exceptions, special items I create myself to either serve a story purpose, or to be components for enchantment later on. 

It depends on the setting. In my setting of Novaspezch currency is only worth what it can be smelted down to and be repurposed for tools or weapons; in the sewers of the City of Nod rare stones get washed up in the waste all the time, but what is desperately needed is fresh food and medicine. For games outside of those settings, I liquidise assets into gold unless the party tells me they'd prefer to keep it.

Even then, this is something I discuss with the players at Session Zero. I want to know if they're OK with shopping and all that it entails: haggling, inflation, trade and so on. Some groups prefer to skip all that, and others want to roleplay their shopping sprees. Either works for me.

My players love to shop, so I let them during downtime. All treasure (gems, art, etc.) counts as gold and can be used as such with a willing merchant.

I don't bother with exchange rates because the bookkeeping annoys me, but I do introduce the concept of resale value and markups if players try to sell weapons and armor to vendors - which I mostly do to discourage them from doing it. A healing potion might cost 50gp, but an herbalist needs to make money on it, so she won't buy it at cost. Ends up being a better deal for my players to keep or use the loot they find rather than try to make a quick gold.

As the above posters, I just consider it gold and trade it freely with no exchange rates or anything.Role playing shopping is about as fun as irl shopping, for me at least, so I try to avoid it (not saying others are wrong to like it, but not to my taste). About the only exception would be if something can be used as a spell component, but then it’s kind of taken out of the treasure pile. 

I allow player characters to sell treasure whenever they interact with merchant interested in buying them. Often it's handled more abstractly and just let them do direct conversion based on value in gold pieces.

I haven't "perfected" it, but my approach plays around with treating finding a buyer for treasure the equivalent of the "selling a magic item" downtime rules in XGtE.  I sometimes play around with advantage and disadvantage with backgrounds.  Someone coming from a lower social economic level of experience isn't necessarily going to know how to find the best route to obtain the best price of the goods.  A background that would presume experience either with high value markets in general or the specific type of item may have connections.  Where they try to sell it, small village vs. cosmopolitan city, local contacts, all could factor.  So it's more gamed than role played, but there's some discussion of how they're going to do this when it comes to making the sales.  

And the table gives you fun with the complications.  I've also come up with further complications to include the original owner of the property or clear heir to the property as birthright comes forward ... we've never had a Battle of Five Armies over anything (which was basically probate court via force of arms), but there's some dilemma as to debating restoring the property to rightful owners or making the best profit.  Thieves guilds could jump the party if they're not at all talking security precautions (talk to real world jewelers or people who actually deal in gems and precious metals, this stuff still happens).

Anyway, treasure in general can reward the game via stories in a way that I think is more valuable to "the game" than GP points, even if the party is mercenary.  Use treasure to keep the game's story moving, not as GP "points" which in 5e don't have much value in game terms in the first place. 

The simplest way is just to allow it to count as the equivalent amount of GP as several people have said.  

I also use the idea of different currency systems on different continents/worlds.  My favorite currency is caribou bones (long bones cut axially) and whale ribs in an Antarctic area.  They are bulky (one dog-sled can only carry two whale bones and it would be encumbered), weird and make sense in that area.  You can have a lot of fun with different currencies.  Dragon Lance used steel coins; gold was nearly worthless there.  If you use different currencies, exchanging them is a great way to make your players poor (what bank set in a Europe-like world would exchange gold for bones???)  

On another rabbit trail, gold should be heavy.  1000s of GP should be a hundreds of pounds.  I never played with that as a kid and had characters with millions of gold, but that doesn't make much sense either.  

If you are being realistic, no weapon merchant would take an oil painting for a magic sword.  What on earth would he do with the painting?  How about an intricate carpet or a statue???  Exotic items would need to be sold to a middleman and converted to gold (at a heavy loss, at least 50%, like a pawn shop) before the PC could buy something with it.  This is less fun for most people, but far more realistic.  Expensive items have very limited markets and no sane person wants to be stuck with something they can't offload (even most corporate bonds are traded so infrequently in today's market you could be stuck owning them for a VERY long time; one of many reasons no to buy them).  

As an aside, I have very few magic items for sale in my world.  And there are absolutely some snake-oil like products that are total duds but cost a lot of money.  I think this is also very realistic.  Even today, people get conned into buying faulty goods and it was more common hundreds of years ago.  Buyer beware!

It depends a little bit on the treasure, if there is a reason to make it more in depth, like its a particularly unique magic item or something I want to use for flavor I'll have them have to seek out a specialized shop in a big city or something and we will roleplay and haggle a bit, but I try to limit that because it can really bog down the session going through item after item doing that. For the majority of stuff, things like jewels or mundane items like basic weapons and armor and low level magic weapons and armor we just do a fast forward when they are in a town that they could reasonably sell the items and they give me a list of which items they are selling and I tell them how much they got for them in between sessions and we move on.

I should have mentioned, despite my long post, my default is to give them 50% of declared value, because that's easiest.

In my world there is generally enough trade that Non magical goods can be sold off fairly easily for 50% of purchase price. Gems & jewelry goes for 75%. Art objects and magic are different. First given the suggested costs of magic and the costs of making the item that are given making magic is generally a loosing deal - they sell for less than the cost to make unless you get some really good rolls on the sell price. If you’re trying to discourage making items that makes sense but not for anything else. So I built my own tables of cost to make, cost of item and rarity of item ( let’s get real an item like a ring of protection that adds to both AC and saves should not be more than uncommon as lots of folks are going to want one and every class can use one causing competition for them and driving the prices up. Special use items like a trident of fish command might actually not cost that much to make but are very rare because they are so seldom made but the cost to buy may be low because the shop/person selling just wants to move it along and clear enventory space. Hiring some one to make such items generally costs at least double the cost to make as the person wants to be well paid for their efforts. I also have a continent spanning organization that specializes in buying and selling high value items, artwork and magic as well as contracting for production of such items on request. They run auction houses in the larger cities. You can sell the item to the group for 75% of estimated value and they then take the risk or you can put it up for auction with them taking a 10% fee for the auction and security of the item but items can earn over 100% of asking price- sometimes well over. Players can choose how they want to deal.

My advice is to ... do whatever your players find fun. 

But more realistically, I believe that if the characters are doing a thing, it should advance SOME kind of plot.  It could be a side story, it could be to seed them with rumors to pursue, it could be to release some kind of evil onto the town (as can happen when the cleric smashes a magic 8 ball that contains the soul of a necromancer).  There are all kinds of things you can do to make the "selling of goods" interesting.

For my money, on the other hand, I'd rather spend 5 minutes doing a quick cash tally and conversion, then to make them play out selling off every piece of art they got.  That said, I would never trivialize GETTING the artwork out of the dungeon.  Yes, this painting is worth 2000 gp.  It's also 4x6feet in a 40 lb gilded frame.  Tell me again your plan for getting it out safely?  

When we get odd loot like some mentioned, artwork, statuettes, jewelry and such, each member claims select pieces, without "knowing" what the value is.  We've tried to assess stuff and we have to make a roll, (History sometimes, or flat Intelligence others) to see if we might know or recognize a value for something.  As a result, our gold pouches vary in value quite dramatically at times.  Also part of that and a result of the sometimes wild range of wealth we had, we developed a "group loot" which we now use to buy stuff the whole group uses (healing potions, rations and such)  Mind you nobody ever got upset or mad when we all had different treasure values we'd claimed, and in fact, we would often have a laugh at how unbalanced WE had made it.  My Monk, at one point, had like 80 Platinum and 150-odd Gold, while the others had maybe 30-40 Gold each.  He spent like a baller for a while, buying our mounts, supplies and paying for the Inns we stayed at.  Everyone RP'd it, looking at him oddly for being so free with his coin.  To him, he didn't value coin, aside from it's ability to get him some stuff he needed.  If his new friends needed stuff and he had coin, he bought it.

I like Gems to have a special place in the D&D treasure space, and therefore I track gems in my game.  But the rest of the treasure, if the players wish to convert directly into coin once they reach a town or city, I just let that happen.  I figure if they don't want to mess around with it, then I'm not going to make a big deal out of it.  I was in a campaign where I, as a player, didn't want to convert stuff, partly because I was flush with coin anyway.  I decided since I had more wealth in coin than I could use already, I wanted to keep the individual items and remember the story about how they came into my possession.  The only risk would be that the original owner might come along and expect me to return it for nothing or a small fraction of the value, and I might not feel so generous.

I like the players seeking out jewelers and all that.  After a few encounters of dealing with gem merchants, they start to get a feel for what the gem(s) are worth, but they don't know until they have it evaluated.  I think that adds suspense to the game.  Maybe the gem is a special gem with a lore all its own.