Hi Carrie,
They need to be kept moist. I keep them in the fridge in the fruit until I'm ready to trade them. Then I remove them from the fruit keeping them in a damp paper towel in a baggie. They will start to sprout in a few days at warm room temp(on top of fridge.)
Just so you or anyone else wants to know, most citrus does not come true from seed. Key Limes and Kumquats are two that do come true. Plus they can both be easily grown in pots. I'm sure there are probably a few others that I'm forgetting/not familiar with.
Remy