Buying Bitcoins (the newbie version)
This page aims to be the best resource for new users to understand how to buy Bitcoins. The existing Buying bitcoins page is too complex, and not noob-friendly.
Intro
You can't reliably buy Bitcoins using PayPal or credit cards, because it is risky for the seller, and therefore few sellers will offer this. There are several ways, depending on your location. Many sellers online will trade bitcoins for moneypak codes. See http://www.moneypak.com/
Via Bank Transfer (US)
Coinbase allows you to buy and sell bitcoin by connecting any U.S. bank account.
Finding a direct seller online
If you can find another person that is willing to sell them to you, you can transfer him money via whatever method (including PayPal), and he'll send you the Bitcoins. The following websites can be used to find direct sellers online Bitcoin OTC, Bitcoinary or the Currency Exchange Forum Section
Physical Trading
You might be able to find an individual you can Buy bitcoins from locally.
Bitinstant
You can buy Bitcoins via cash deposit or bank transfer using BitInstant. Here is a video tutorial explaining BitInstant: http://vimeo.com/44849463
Exchanges
The largest and most trusted exchange is MtGox. For a list of other major exchanges see Major Exchanges
PingIt (UK)
UK users can use Barclays PingIt to purchase bitcoins from blockchain.info.
Avoiding Scams
Before using any service it is a good idea to look for reviews and feedback from previous customers. This can be done by simply googling the name of the website or company. The bitcointalk forums are also a good place to find discussions and reviews about services.