I did my first chargeback ever a few weeks ago, and I've had a credit card for about 25 years. The key thing is that you have a limited amount of time to do this, so pay attention to dates. I think that 90 days from the date that the charge first appeared on your statement is typical, but check to make sure. When I did my chargeback, there was a ton of stuff to document, so make sure that you preserve *everything*. At minimum, you'll need a copy of the order and any communication that you had with them. Send them email, preferably using an account like Hotmail or Gmail. If you call, make a note of the date and time, the rep that you spoke with, and any details that they told you. And if you are going to do a chargeback, do everything that you can to show a "good faith" effort with the merchant. This means contacting them several times using both email and phone, and make more than one attempt with each. Then when you make your claim, instead of saying "these jerks screwed me", just point out everything that you did to work with the vendor and then say, "I did everything that I could to resolve this with the vendor and have run out of options". Your bank will love you for this because it helps them to justify the chargeback decision.
One final note - chargebacks aren't guaranteed. They work a large percentage of the time, mainly because the cost for the vendor to research what happened is much higher than the loss that they take on the product, and they are still likely to lose. When you put together your documentation, keep a copy in case you lose the case with your credit card company and need to take legal action against Dell.