There are two types of liposuction currently being used in the US. The first is older and more well studied, and that is tumescent liposuction.
In tumescent liposuction a small incision is made and the skin is lifted away from the facia and fatty tissue layer and saline mixed with anesthetic is injected. A canula is used to shred up the fatty tissue which is similar to balls of tapioca, and then the fluid, blood and fatty tissue are extracted under vacuum pressure. A compression garment is then used to achieve the best results. Pain, draining, bruising and possible uneven results are common.
Laser assisted liposuction uses a laser to more precisely remove fatty tissue with less damage to surrounding structures. There is a more even final result and less bruising. The long term effects of laser use have not been studied.
Best of luck.

