There are two basic types of RC helicopters, ones with two main rotors that turn counter to each other, which have no tail rotor, and ones that have a single main rotor and a tail rotor. The tail rotor is there to counteract the torque effect that the main rotor creates. A gyroscopic controller is used to coordinate the main and tail rotors so the helicopter can fly straight. When this system is not working correctly the helicopter will spin in circles.
Remove the main rotor blades, throttle up the helicopter while holding it in your hand and twist the helicopter from side to side to determine if the gyro is working. The gyro should make the tail rotor spin faster when the helicopter twists; you will be able to hear a difference. If the gyro does not appear to be working, replace it. Some gyros have a sensitivity adjustment screw; try making small adjustments if possible.
Check the tail rotors and see if they are connected correctly. If the tail rotor blades are not pitched correctly they will not be able to hold the helicopter still.
Test the tail rotor motor and see if it seems strong and responsive. Brushed motors, like those commonly used to drive tail rotors, can wear out in a relatively short time. Replacing the motor may solve your problem if the gyro seems to be working.
Check the trim on your transmitter. Ideally the trim should be in the center of the stick movement. You may need to dial in some extra right trim or you may find the trim is set too far to the left.