Although the ShaftofWisdom has pretty thoroughly answered your question allow me to add a little more in depth opinion. Just to be clear you can't really order a full keg any more unless you're a bar or some shit. Now what is typically refered to as a "keg" is actually a half barrel (15.5 Gallons or ~165, 12 ounce drinks). You wont get all of those 165 drinks but we'll get to that later.

Order your keg, one or two days in advance should be plenty of time. There will be a deposit for the keg (~$30) and tap ($30-$50) as he mentioned previously. When you pick up your keg pick it up as early in the day as you can so you can tap it early and let the foam settle. Now treat this thing like a god damn nuclear warhead, no seriously don't shake that shit up at all. Get a friend to go with you so you can have some help bringing it inside, they are made of very light aluminum but completely full they weight more than 100 pounds.

Using a large plastic trash can works great but it can be a pain once the ice starts to melt and the keg sinks to the bottom of the can. I use one of these bad larrys. It's simple and usually cheaper and gets the job done just fine. Add 5 or 6 bags of ice, placing some one or two on the bottom before you place the keg in and you should be on your way. Note: the colder the beer the less likely it is to foam.

I really don't like the standard tap as it ends up wasting a lot of beer by producing a lot of foam with the initial tapping of the keg as well as throughout most of the keg. In other words you end up losing a lot of your beer. If you really want to ball out get a CO2 system, they are a bit more pricey but if this is an ongoing endeavor it will end up paying for itself. But whatever you do please don't get one of these taps they really blow.

I'm going to assume that since this is your first time getting a keg you probably won't be needing the CO2 system so let's start with the normal tapping system and procedure. Look at this picture and notice the circles, I will be referring to these two circles as I explain how the actual tapping procedure occurs. First of all make sure that the lever in circle A is upright as it is shown in the picture. That black handle with the upward arrow pulls out away from the tap and allows it to be pushed back in to lock it into place. The bottom silver part has threads that will allow it to be screwed onto the keg. Line those threads up with the threads on the top of keg and screw it in. It will only turn about a half turn or so. Then take that black lever pull it out and push it down to lock it into place.

Yay! You just tapped your first keg, now don't pump the shit out of it or it will only foam, you really only need to pump it when you see the stream of delightful beer coming to a slow stream. If you over pump it guess what? Fucking foam! The first five or six glasses will probably be foam, more if you've shaken it or disturbed the little foam gremlins inside the keg. But again tap that shit early and let the foam settle.

Have fun, and do a keg stand for me!

EDIT: Spelling and Grammar