My first question is whether or not this is a front-wheel-drive car. It makes all the difference in terms of how you handle the vehicle in a skid.
In a skid, the rear wheels spin out and try to overtake the fronts. If you are driving a rear-wheel-drive vehicle, you get the skid under control by steering in the direction of the skid – turn the steering wheel in the direction the rear wheels are moving in – and let up on the gas. You don’t apply the brakes until the car is under control.
In a front-wheel-drive car, the rear wheels are not driven. Letting up on the gas will make the skid worse. In a stick-shift car, you need to either keep your foot on the gas, give it more gas, or push the clutch in. Pushing the clutch in will often right the car immediately.
For traction, you need to keep your RPMs as low as possible without stalling as you ease up on the clutch. Sometimes you can try starting off in second gear, as that reduces the torque to the drive wheels. This is something that just takes practice. It’s harder to rock a stick-shift car out of a rut, as reverse is usually awkward to get into.
It’s also important to rev match your shifts. You should be doing this anyway, but you’ll have fewer traction problems in the snow if you learn how to do this. Shift at the lowest RPM that will keep the engine above bogging speed. Slipping the clutch through turns will help keep the car under control. With a front drive car, control understeer by pushing in the clutch. With a rear-driver, give it a little gas if you’re understeering.
Last but not least – if this is a performance car, get some winter tires. Tire Rack has winter tire/wheel packages for most vehicles.