Most often beer is cold-crashed in the carboy (or bucket) before kegging. It doesn't have to be but it really clears the yeast so that the there's less yeast sediment settling to the bottom of the keg. Whether you cold crash or not, you can force carb and let it sit at room temp for a while.
Definitely purge your keg...pressurize to 10 lbs or more and purge. Do that a couple of times and let it sit under pressure for a few minutes while you get everything set up to transfer.
When you're ready to transfer, set the keg in place, release the pressure and pop the top. Inside the keg will be all filled with smokey mist. Proceed to siphon and keep your racking cane off the bottom so that you're getting clear beer with no yeast. I use a spring clamp on the racking cane to hold it at a certain level. I always prop up one edge of my carboy and direct the siphon to the lower edge. As it gets toward the bottom, I'll lower the siphon until it almost touches the yeast cake/trub.
When your keg is full, replace the lid, put on a little pressure and then purge it to make sure there's no oxygen. Then you can pressure it up as you see fit.
I tend to use high pressure (30-40 lbs) overnight and then adjust over the next day or two as needed. If it's cold and you leave it on the CO2 hookup overnight at 40 lbs, you can purge, reduce pressure and serve the next day. If you plan to let it condition at room temp for a week or two - and that's a fine option - leave it on the hookup at 20lbs or so and it'll be carbing as it's conditioning.
Cold conditioning is important too because it helps the beer get really good and clear. Most beers will probably benefit from a week or maybe two of room temp (it totally depends on length of secondary/bulk aging) followed by a week or more of cold conditioning (lagering). IPAs, Porters, etc need less and clean Lagers, etc need more..up to a couple of months of cold.
Here's a carb chart that's very useful:
http://www.kegerators.com/carbonation-table.php