We haven't used ours yet, but we ordered it from here: www.jrpass.com/ They have plenty of information on how to use it, but there were a few questions that I wanted more specific details on, and I found them on the official JR pass site: japanrailpass.net/eng/en001.html
You have to buy it before you leave. There are different places you can buy it from (as explained here). On trains with reserved seats, you can make a seat reservation at a reservation office (as explained here).
As for which pass to buy, we decided to get a 7-day pass even though we'll be in Japan for 2 weeks. We'll just use it for the 7-day stretch in the middle where we're traveling longer distances. Tickets within the city tend to just be a few hundred yen, so I didn't think we would come anywhere close to spending enough to cover the additional cost of the 14-day pass. Also, since we're spending a lot of time in Tokyo, buying individual tickets will allow us to use the non-JR railways if we want. We'll just load a few prepaid Suica cards for our Tokyo trips.
Also, hyperdia.com is great for researching train timings and prices, and they allow you to exclude the shinkansen routes that aren't covered by the JR pass (NOZOMI, etc).
And japan-guide.com has some general info about how the transit systems are set up in different cities.
Yes to using Hyperdia! It's really helpful. Gilli covered it, but just to answer your questions:
What pass do you recommend? The shortest JR pass is for 7 days. Do the math with your trips and the cost of the pass because it still might save you money. We also used it for day trips from Kyoto.
For getting to and from Narita and getting around Tokyo we got a Suica + N'Ex card, but it looks like they're not doing that combined anymore. So I suppose you just get those separately at the JR East office at Narita. If you get the JR passes and activate them early you could also use the JR trains within Tokyo, which isn't necessary but will give you more options for getting around.
In Kyoto we took the bus everywhere (the subway isn't terribly convenient), and we'd just buy all-day bus passes at our hotel every morning.
Do we buy it before we leave? Who do you buy it from? Yes, you have to. I got ours from JTB travel because their office was very close to my office in Seattle. I went in the morning to fill out the order form and picked up the vouchers that afternoon. They you pick up the actual passes at one of the offices in Japan. I forget if we had to tell them which office we wanted to get them from.
Do you book seats on cars beforehand? On the shinkansens, but on the smaller regional trains you don't have to. If you take the Narita Express (N'Ex) you have to book seats. You can do all the reservations right before you get on the train.
How does this all work? It's really easy! The trains are all nice and efficient.
Travel is fatal to prejudice, bigotry, and narrow-mindedness, and many of our people need it sorely on these accounts. Broad, wholesome, charitable views of men and things cannot be acquired by vegetating in one little corner of the earth all one's lifetime. Mark Twain