Gemstone are stored in your purse, and the Greed are able to steal gems left on the ground. When you are hit by a greed or if you drop your belongings, coins are prioritised. But if you have no coin left, your gems will drop. There's no gems on the first level. In the second level, check the far left and right of the area, right to the end, and you will find 2 to 4 gems chests. Chests will respawn after time, so open each gem chest you meet. Once you've upgraded your camp enough times, there is also a very small chance of receiving gems from the priest. Acquiring a gem by Day IX grants the achievement "On the Ninth Day".