It's really hard on your suspension. It's designed to absorb up/down movement, not lateral movement. When you're drifting, you're essentially pushing in really hard on the bottom of the outside rear wheel. That's tremendous sideway stress to a wheel. If you have low profile tires, you also risk damaging your rim as the tires will rolll underneath it a bit when pushed like that. That's why the Japanese drifters lower the psi on the tires to give it more sidewall contact patch.
With the warnings out of the way, there are quite a few ways to induce oversteer. Drifting is essentially throttle-steering your car once it's in overstter condition. What's throttle steering? Well... uhmm.. go to a car control clinic. They'll have you go around in a circle really fast, and you'll notice that you can increase the diameter or decrease the diameter of the circle by adjusting the gas pedal without turning the steering wheel. It has racing application too, because you can turn left/right in a turn by using your throttle, not your steering wheel. Driving schools rule!
How to induce oversteer? Well, find a real wet area. Dry spots are too harsh on your car. You can 1) pull handbrake while in a turn, 2) full throttle to spin the rear wheel while in a turn, 3) in the middle of a turn, abruptly lift off the throttle, then re-engage throttle once the tail have spun out.
My recommendation is first go to a BMWCCA sponsored car control clinic. Learn what understeer and oversteer feels like, and how to control it. After you're familiar with what it feels like, then try it out on a wet parking lot. Don't try drifting around on the street! Your turning radius may be a lot larger than you anticipated and you'll hit curbs, real hard.
What's the difference between understeer and oversteer? In understeer you see what you're going to hit. In oversteer you have no idea what you're going to hit.