To check this, take out the bulb from your car. Refer the owners manual for instructions on how to get the light out. Once the bulb is out look at the wire filaments inside. If they are broken, the light is probably burnt out, but if they are still connected, the bulb is still good.
If you have determined that the wires inside the bulb are ok, look at the metal connection pieces at the bottom of the bulb. Often times this area can get corroded or burnt. If you see and signs of this, try to scrape off the corrosion. You can use anything that is small such as a screw driver or a nail. Also check the socket where the bulb plugs into. If there is corrosion in there, try to get it out with a small screwdriver or tool.
Once it is clean, put the bulb back into the socket. Turn on the power in the car and test the turn signal. If it works, you are good to go. If it doesn't work, you can try cleaning it a little more. If it still doesn't work, you may need to replace it with a new bulb.