EDIT: To check your credit report, you can go to
AnnualCreditReport.com. You can request one from each of the big three. I usually request it once every 4 months, so I can see how my credit's doing 3 times per year. The Federal Trade Commission's website has more info:
http://www.ftc.gov/freereports
Dell offers credit as well, though as mentioned before, any sort of store-branded line of credit (such as Macy's, Best Buy, Dell Financial Services) can harm your overall credit score.
It
is good to get a major (Visa or Mastercard) credit card to build up credit for the day when you'll want to buy a house or car, but you wouldn't want to use one of those on a computer.
All credit cards have a closing date for the month. After that date, you'll receive a bill for the charges, usually due 15-25 days later. Some companies send the bill later than others, shortening this window.
Any portion of the balance not paid off in full by the due date is subject to finance charges. There is always a minimum required payment - missing that will usually cost you a late fee. However, there is also the nasty concept of "universal default", where a late payment on one card can cause the rates on all other cards to go up.
The safest way to use CCs is to only charge what you can afford. That is, don't buy it if you don't have the cash to pay for it. As long as you pay off the card in full by the due date, you will not incur any finance charges.
I have a Visa that gives me 2% cash back on groceries, gas, and drugstores, and 1% on everything else, and then I also use a Discover card, which has 5% cash back on various categories throughout the year. Discover isn't widely accepted.
Some (usually local or smaller) merchants do charge more for credit cards than cash (or disallow the use of certain types - like Sam's). This is because retailers must pay a service fee for every credit card transaction they process. While larger businesses eat this cost, others prefer to pass the cost onto the consumer.
I'd agree with the folks who are suggesting you pay for the computer in cash, though you probably ought to shop around for a decent credit card, as well. It's easier to get a card while you're in college, and if you use it wisely you can build up your credit pretty well by the time you finish.
My sister didn't apply for a credit card until she was out of school, and by the time she did (at age 23) she couldn't get more than a $2000 credit limit. She also couldn't get approved for a loan to buy a car. It's a very complicated industry, designed to make as much money off of you as it can, but you can (and should) use it to your advantage if you're careful.