I bought a Suica card on Saturday evening, after going to karaoke in Shibuya with Chihoko, and some friends from Leeds University last year, when they were on an exchange. It was a very fun evening, with renditions of MC Hammer, Sir Mix-A-Lot, and the Titanic theme tune.
Suica cards are like credit cards that you can use for trains, buses, and even some vending machines. It stands for "Super Urban Intelligent Card" and you can charge them with money at ticket machines in any station that you can use Suica at, which is nearly all in Tokyo, and lots in other parts of Japan too.
After charging the card, you just swipe it over the reader as you go through the ticket gate. You don't have to take the card out of your wallet for it to read it. I've even seen people in a hurry just slide over the ticket gate, and the machine read it through their clothes.
After swiping it, the remaining balance on the card will appear on the screen, and when you leave your destination station, you swipe it again, the money is automatically deducted, and the screen displays the cost of your journey, and the remaining balance.
You can buy Suica cards at major stations that support them for Y2000. Included in this price is a deposit of Y500 (which you can get back if you take the card back to a station office), and the other Y1,500 becomes the first balance on the card.
Suica cards are completely interchangeable with Pasmo cards (I used to have one but I forgot to bring it back with me), but with Suica you can also get special types of card where you pay a set fee for unlimited travel between certain stations (定期, teiki). This is really good for people who travel to work or school by train every day, but I wouldn't use trains often enough to make it worthwhile. Students can even get a discount by showing their school ID when they purchase it from a station office.
Suica cards make train travel much more convenient, so even if you're in Tokyo for a short time, it's definitely worth getting one. As you can get the deposit back, it's basically free!