There are all sorts of convoluted ways to buy bitcoins. For your first purchase i would recommend www.bitinstant.com or localbitcoins.com.

When I have used bitinstant, here is what I do.
First set up an account at Mt.Gox. Now when you go to bitinstant they are basically walking you through a deposit into Gox's bank account. You will be given the info you need to hand over cash at one of many locations, such as a Walmart. By the time you drive home your money is likely already sitting in your Mt.Gox account. (Don't lie on the forms or it may not work) Now that your account is funded you can try to get a good price buying BTC at Gox. It is not a cheap way, but *easy.

Localbitcoins is a different idea altogether. Here you try to find a local person to sell you bitcoins in person. You arrange to meet at a coffee shop or something and bring your laptops. You hand over cash and the sellers sends the coins right there. Then you have coffee together and talk bitcoin.