Refrigerator ice makers can malfunction for a number of reasons and there are a number of ways to troubleshoot the issue depending on the problem. The key is figuring out the problem first.
Inlet Valve Issues
According to PartSelect.com, one reason an ice maker may not be producing ice is because of the water inlet valve in the refrigerator. This valve is what turns cold water into ice, and it can become blocked with a number of substances. Removing the valve and cleaning any debris or purchasing and installing a new valve usually solves the problem.
A freezer thermostat that is broken or not set at a low enough temperature can create issues with ice makers. The same holds true if a refrigerator's defrost thermostat is not functioning properly. The first step in solving either of these problems, according to PartSelect, is to set the thermostat to a colder setting. If that doesn't work, odds are the thermostat will need replacing.
If adjusting, repairing or replacing valves and thermostats doesn't solve the problem involving your ice maker, it could be a sign of other, more complicated issues. If that's the case, it would be a good idea to call a refrigerator repair service.