How long do I need to carbonate a keg?

The delivery pressure depends on what style you're serving. Myself, it's usually always something of the IPA variety served anywhere from between 38-42 degrees F. I keep it simple. When I keg, I dial up the pressure to 30 PSI for 24-36 hours, then dial back to 10-12 PSI for another 24 hours. I've never had a bad pour using this method and I tried many different techniques. You will want to heed the advice about using the correct length of delivery hose, though, as you will definitely have foam issues if you use a length that's too short. I would use one of the many calculators available on the internet to establish the correct measurements for your particular application.

Very interesting discussion. Regarding the potential pressure issues the device on the link below may help. I hold my beer at ambient, use a flash cooler and one of these gadgets in between the cooler outlet and the tap it works good and I dont need nor do I have space for a kegerator. Not suggesting you buy one from this site but just offering a solution to possible foaming.

http://www.micromatic.com/draft-keg-beer/ez-balance-pid-802991KS.html

You can go from uncarbonated in the fermenter to carbonated in the keg in about 15 minutes.

The key is agitation. Just the other day I witnessed a guy take a batch that had been cold-crashed, racked it to the keg, agitated, and served properly carbonated beer in 30 minutes (we had an issue with racking, so took a bit longer).

Basically, you turn on the CO2 and adjust the screw on the regulator to set it based on one of those charts you can find on the internet where you select the number of volumes and the temperature and it gives you the PSI to set. You will hear gas bubbling inside the keg. It will continue for a little while and then stop. This is because the keg is standing upright and there is only a small amount of surface area for the CO2 to dissolve into. To increase the surface area, place a towel on your lap and set the keg on its side on your lap. Shaking or rolling the keg will start the flow of gas again. Eventually no matter how much you roll or shake the keg, no more carbon dioxide will go into solution and you won't hear any more bubbles in the keg. Your beer is now fully carbonated, although it's best to let the keg set inside your kegerator for a few hours to settle down before you try to dispense it, you can be drinking beer right away, albeit with a bit of head on it.

Some of the above stolen from winning-homebrew.

I've had success with 32-25F beer set to 30PSI for 24-36 hours. You can cut that time down if you are willing to occasionally roll the keg on the floor while you are charging it. After 36 hours, bleed the pressure down to serving (11-14 PSI depending) and pour a glass. It will blow off a fair bit of the carbonation into the head foam, so the beer will be a little under-carbed if you let it sit in the glass for a bit, but this will get you in the ballpark fast.

It takes at least 3 days to be carbed with the sit and wait method you describe. But a week is really what you need to truly "equilibrate" to the pressure being set. In your case of shooting for >3 volumes I would definitely expect it to take a week.

The beauty of kegging though is that there is no reason to not pull a half pour after day one, two, six etc etc. Then you can see how long it takes, and if 3.2 volumes is to much you can stop it right where you want it.

There is a faster carb method that involves setting the regulator to 30-35PSI and shaking the keg of beer for a few minutes, let it rest for a few, then shake again. You keep doing that until the beer is carbed to where you want it. This is a great technique if you finish fermenting a beer on wendseday and you want to bring it to an event on friday. The only issue I have had with this method is that its fairly imprecise and I end up with over carbed beer, then I am bleeding pressure off. It works but it takes more effort that I like to invest. The sit and wait period seems to work fine for my style.