Instructions
Load up "Burnout Paradise" and select a car. You can power park with any car in the game, but "stunt" class cars are the best for beginners, as they have good speed stats and are built for drifts and e-brake turns.
Drive around Paradise City and look for a parking space. Search for a road with little traffic and with cars parked along the side. The dam area in the south of Paradise City is one of the easiest places to power park, as there are walls along the sides of the road that make power parking much easier.
Find two parked cars with a gap of two or three car lengths between them. Drive toward the space from the opposite side of the road at an angle of about 30 degrees. You'll need a good run-up, as you must to be going fast (and have enough space) to pull off a 180 degree e-brake turn.
Hit the e-brake button (A on the 360 and square on the PS3) when you are alongside the gap between the two parked cars. Steer into the space so that your car spins around 180 degrees and faces back the way you came. If you're parking against a wall, you should hit it and stop dead in the space. Avoid hitting either of the parked cars (this will void the stunt), and if you're not parking against a wall, stop exactly parallel to the sidewalk.