You start by having it checked for codes. The light comes on because the computer has detected a fault. You need to know the code to know what to repair.
If it is making a rapid clicking as compared to the slower intermittent clicking. One of your turn signal bulbs need to be replaced, normally it will only do this when the bulb is not working at all.
Many car parts stores will connect a diagnostic scan tool to your car and read the codes for nothing if you buy the necessary parts from them to make the repairs. You can also purchase a scan tool...