I usually just replace the ice maker.
If your ice maker has stopped producing ice completely, check these, in this order:
It may be turned off. Look for the wire along the right side of the ice maker that looks a bit like a coat hanger. If the wire is in the raised position, the ice maker is turned off. If so, try one of these:
If your ice maker has a small red plastic lever, lower it to lower the wire.
If there's no plastic lever, simply lower the wire.
The ice maker fill tube may be blocked with ice. If so, melt the blockage using a hair dryer-but be careful to not melt any plastic parts! Also replace the water shut-off valve or water-inlet valve, or both, if necessary.
The ice maker head assembly may have broken parts. Look to see if the gears are broken. Check to see if the small plastic arms that rest against the ice rake are broken. If the ice maker head assembly is modular and you've found broken parts, you can just replace it.