I had this happen to me once. The easiest thing is to replace the control stalk on the column. I tried to use one from a parts car, but you'd have to find another car the same year and trim level as your own and even then, it's hit or miss with the way they're wired up internally.

If the signal is constantly blinking, the flasher relay is fine. It's because something in the control stalk borked and is stuck closing the circuit.

There's four bolts going into the back of the steering wheel to remove the airbag, but be sure to disconnect the battery and let the car sit for ten, fifteen minutes to be sure the SRS system discharges.

Once you get the airbag out, you remove the center nut on the wheel and wiggle the wheel back and forth as you pull on it. It will more than likely come off when you least expect it. ;)

Basically, aside from disabling the SRS system, it's all pretty straight forward and common sense stuff. You'll see. There is really no disassembly of any components, just removal. Then you slide the new control stalks back on (did I forget to mention you'll have to buy the turn signal and wiper controls for a grand total of about $125) and reverse your removal steps.

On the plus side, new turn signal and wiper controls make the car almost feel new again. Not old and borked like it really is. :7