Check fuses, which are usually located in the compartment and/or under the hood. Then verify the cable is in good condition and not too tight. Lastly, take to shop.
If it is located on the steering wheel itself, it could be as simple as a fuse, relay, or switch. If the control is located on the turning signal shaft...then you are in big trouble, as the entire part (500 bucks) needs to be replaced.
The light comes on but the cruise control does not engage, test ALL fuses with a testlight, testlight or voltmeter,pump circuit check,perform fail-safe check system,break or clutch cancel check.streering switch check
The basic starting point would be a bad switch. I dont know what kind of car you have but switchs are notorius for going bad so just pop it out and use continuity tester on it.