I soak mine in moisturizing eye make up remover. This gets rid of the glue and the mascara and keeps the lashes hydrated so they last longer. I use a q tip or cotton pad to clean them off, gently reshape, and then put them back in their original container to store, as tenngal suggested.
Here are a few tips about caring for your false eyelashes:
Cleaning False Eyelashes: If you applied a layer of mascara after applying your false lashes, you need to clean off that mascara, or your false eyelashes will become brittle and break. You also need to remove the adhesive from the backside of the lashes, which you can do by gently lifting the adhesive with your fingers and gently pulling it back on itself until it comes off. After the adhesive is removed, lay the eyelashes on a tissue and use a Q-tip dipped in eye makeup remover to rub the eyelashes from root to tip until they are completely clean.
Storing False Eyelashes: The way to store false eyelashes is to place them back in the case they came in when you purchased them—that case already has a ridge that you can stick the eyelashes on to keep their shape. If you've already thrown out that case, you can use a small matchbox to keep them protected so they are available the next time you want to use them.
Hope this helps!
Have a great day!