There are two basic ways that have worked for me. One is to simply set it at 12 psi in my kegerator (at 40 degrees) and try it in a week. In a week, I pour a couple of ounces, and it's almost all yeast sludge. Then I dump that and pour a glass. It's usually pretty good, but carbed up better in a few more days.
If I"m in a huge, huge, huge hurry, I put it in my kegerator at 30 psi for 36 hours. Then, I purge by turning off the gas, pulling my pressure relief valve and resetting the regulator for 12 psi and putting the gas back on. I pour 2-3 ounces, again it's mostly yeast sludge so I dump that. Then I pour a glass. It's pretty good, but carbed up better in a couple more days.
I am not one who would shake up a keg to get it to carb up faster, no would I mess around more than once or twice with adjusting the regulator just because I'm in a hurry. I have room for 5 kegs, and I keep them always at 12 psi in my kegerator. So changing it is sort of a PITA for me.
I moved a keg, well carbed and without sediment, out to my cottage today. Just taking it from the kegerator at home to my cottage 12 miles away gave me foamy pours all afternoon. It takes a while for a stirred up/shaken up beer to settle down (like shaking a can of soda!) so even if you tried to quick carb it by shaking, you'd still want to want a couple of days anyway for the beer to be ready.
Broken Leg Brewery
Giving beer a leg to stand on since 2006