The adventurers return from their journey with sacks full of gems and jewelry. They sort through, divvy up what they want to keep and then sell the rest. Depending on how detailed a GM wants to get and what system you are playing, I'm guessing most adventurers are not going to have much of an idea the value of the gems or jewelry. In most adventures there will be a value listed, two emeralds worth 50gp each and a pearl broach worth 100gp. And so on. For someone who wishes to add a little depth to the selling of these precious stones please take a moment to read my simple and complex systems.
Simple: The simple version is to give 50% of the value for finished stone. Those that need to be cut 25%. Jewelry is a finished product and depending on the condition a merchant will give 50% of the value or if it is a rare piece up to 75%.
Complex: Gems and jewelry are fickle things. Their value goes the way of trends or fashion of the times. Emeralds may have been in last year, but don't be caught wearing those this year. This year topaz is all the rage. So I use a simple equation. The value of a gem that is trending is worth 50% more, those that wear last year's favorite suffer a 50% loss. The one exception to this is diamonds. They never decrease in value.
I use this sub-system of selling to add a little flavor to a campaign setting. Those nobles and richie riches like to show off that they can keep up with the others. Or surpass them in superficial displays of wealth. And it adds a little stratgy for the jewelers and gem buyers. Maybe they chose not to buy gems that were last years because they don't want to get stuck with them. Or you have a thrifty merchant who is buying all the emeralds up at a lower cost and willing to wait the years for them fall into favor once again.