Ohhhhhhh, boy, what a can of worms!
The "best" way is arguably just the best way that works for you.
Cold beer absorbs co2 better, but you can certainly carb at room temperatures simply by using a higher pressure.
Here's a carbonation table to check:
http://sdcollins.home.mindspring.com/ForceCarbonation.html
For my system, a kegerator at 39 degrees, I find that "set it and forget it" works the best for me. I keg the beer, and give it a shot of co2 and pull the pressure relief valve. That helps purge out any oxygen hanging around in the keg. Then, I give it another shot, check the lid and posts for leaks (spraying with star-san is great!) and then place it in the kegerator at 12 psi. In one week, it's carbed enough to drink, and it's perfect in 10 days to two weeks.
I'm NOT a fan of "burst carbing"- shaking the keg or putting it at ultra high pressure so it'll be faster. In a real pinch, I've set the regulator to 30 psi for 36 hours, then purged and rest to 12 psi, which carbs it up in about 3-4 days. But the beer is better in a week or so.