Some recommend either set and forget, which takes a good week at least, or crank and shake, which is too uncontrollable for my taste. My method is:
Day 1, keg room-temp, flat beer. Stick in fridge, hook up to CO2 at desired pressure. Bleed off pressure a few times to purge headspace of oxygen.
Day 2, keg is now full of cold, still almost entirely flat beer. Cold is key - it will absorb tons more CO2 when cold, which is why I wait until day 2. That night, I crank the CO2 up to 2.5 times the desired pressure - so if I want 10PSI serving pressure, I'll crank it to 25PSI. (Note that this may not be a good idea with high-pressure beers like Hefe - use common sense)
Day 3, first thing in the morning, I bring it back down to desired pressure. It's pretty close to perfectly carbonated at this point, so if you let it sit until day 4 (to avoid excess foaming) you'll be able to serve it right away. However, the next few days will make it better and better as it reaches perfect equilibrium.
After day 3 we want it just slightly below the target carbonation, so it can coast up to the right level slowly without overshooting it.
At first, I did 3X desired pressure, but I kept coming back to a higher-than-set pressure due to CO2 coming out of solution in the beer - so clearly that's too much for me, as it was over-carbed. Note that my batches are 2.5 gallons, and I believe the massive amount of headspace leads to faster carbonation. You may have to leave it longer with a full keg, or use a higher pressure multiplier. After 2-3 batches, you'll have it dialed in perfectly.