Force carbonation is the process of putting co2 into your kegged beer by forcing the gas into it, rather than using sugar.

If you look on the forums you'll find two ways that people force carbonate. I'll call them the fast and slow method.

Fast Method

Set the pressure higher than you want, maybe around 30psi. Shake the keg until regulator stops making noise. Then you release the pressure, and set it to your desired carbonation pressure. This method is very quick, but it could result in over-carbonated beer.

Slow Method

Set the pressure to the desired carbonation pressure and let it sit for a week. This method is pretty much fool proof, but takes a while.

I haven't seen this one mentioned too often, but I think it's a good compromise between getting it carbonated quickly and to the proper pressure. I'll call it the hybrid method.

Hybrid Method

Set the pressure to the desired carbonation pressure and shake the keg a couple times a day. This usually gets it fully carbonated in two days or so.