The quickest route to repair is to have the car plugged into a diagnostic machine which will read off the fault code stored in the ECU and give an indication as to which sensor has failed or whether the fault is more serious.
The system uses inputs from the wheel speed sensors and engine and gear selection to rein back engine power if it thinks the wheels are spinning (like on ice). If you have a faulty or bad signal from a wheel speed sensor the ASR controller can be fooled into thinking there's wheelspin and it'll cut engine power/ throttle and/or shifting of the transmission accordingly, to prevent you from damaging the drive train (or wrecking).
99% of the time its a problem with one of the wheel speed sensors and I'd first check the connections at both rear wheels for any signs of corrosion or chafed wiring. The sensor is located in the wheel hub so you'll have to remove each wheel in turn to inspect them. Make sure the sensor area is clean and free of any debris. You can check each sensor's function by plugging the two output wires into an AC voltmeter and spinning the wheel quite quickly, you should get a voltage signal that increases with rev's.
The ASR light can be triggered by simply removing and repairing one of the rear wheels, because the sensor isn't replaced properly, or there wiring harness gets kinked or something. I once had a rear tire repaired, and then every time I was at 60 MPH or better and there was a strong crosswind, the ASR light would come one. Jiggled the wiring harness and all was well again.
But I'd just take it to a dealer.