Note that this is not the same thing as a savestate. You must first save in-game using the game's normal saving mechanism and then press X to send the updated save info to the "GAME_NAME.sav" file on your card. If you don't press X the save data will be lost. It's an extra step to remember, but it becomes second-nature after a while.
For games that don't have any in-game saving, you won't be able to save in Lameboy either.
Note that pressing L+R to go to the rom menu also automatically saves the SRAM.