An entire diagnostic manual has been written to work on the anti-lock brake / traction control system.
If the ABS and Traction Control Off lights both turn on, suspect a problem with a wheel speed sensor signal dropping out. That is commonly caused by the normal play that develops in the wheel bearings. You'll find dozens of those wheel bearings in the GM dealer's scrap pile.
If the ABS light is not on, but the Check Engine light is, start by having the stored diagnostic fault code(s) read in the Engine Computer. Many auto parts stores will do that for you for free. Those codes will get you into the circuit or system that needs further diagnosis. A common cause of multiple warning lights turning on is a defective generator. Replacing it four to six times in the life of the car is not unusual. If it is not charging the battery properly and must be replaced, replace the battery also. Many professionals are finding out that as they age, they lose their ability to dampen and absorb the huge voltage spikes these generators produce. Those spikes can damage the internal diodes and voltage regulator leading to repeat failures, as well as interfere with sensor signals.