The most common cause of the steering pulling to the side is because one of your brake callipers is seized in the off position and is therefore not working, the direction in which it is pulling tells you which one, if the caliper were seized on, you would be getting smoke from behind the wheel along with the smell of frying brake pad! Another cause however could be to do with the Track Control Arm or wishbone depending on what kind of car you have, this is what attaches the wheel hub to the chassis via a ball joint, what happens here is the rubber bushes wear causing lateral movement and when you brake, it makes the wheel move backwards and causes the wheel to steer itself so pulling the car to one side, if you have a proper jack at home you could quite easily bung your car up and have a prod around although be careful if you do this, if your car has ABS don't rotate the wheel and apply the brakes (wheel off the ground) with the ignition on as this will confuse the ABS Electronic Control Unit (Brain), it will flag a fault in the memory and put the ABS light on which is an instant MOT failure, its a main dealer job to sort which will leave your wallet very floppy!