F7 Load a save state. You will be requested to press a key to
determine which save state you wish to load. Note that the save
state feature is not supported for a large number of drivers. If
support is not enabled for a given driver, you will receive a
warning when attempting to save or load.
SHIFT+F7 Create a save state. Requires an additional keypress to identify
the state, similar to the load option above
Make sure you use LEFT-SHIFT F7 to save to a location. The FAQ don't think it mentioned it.
If still not working, check your setup in MAME. Go see what you have it setup to, or setup it up the way you want it of back to default.
It's a good idea to check the Save State folder in the left field of the MAME GUI first for games with full save state support. Other games that are not in that folder may still be able to do save states, although in this case the stability of the function is not guaranteed.
The defaults are Left Shift+F7 to save and F7 to load. When calling up these functions you then need to pick numbers or letters on the keyboard as positions to save to or load from. For example, you play for a while and decide to save>go Left Shift+F7 then press 1 to save to position 1>you want to continue later>go F7 then press 1 to load from position 1 and get back to where you were. You can keep adding new save/load positions on other keys as you progress through a game to build up a collection of handy save points, or if you're not fussed you can just keep overwriting the same position.
Saved states will automatically go in the sta folder of the MAME root directory if you ever want to clear anything out.