To download games onto the PS3 you need the following:
1. An internet connection to the PS3. This can either be a Ethernet line (like from a cable modem) or it can pick up signals from a wireless hub.
2. A credit card, or some other method of payment (paypal is not accepted)
3. An e-mail account. You have to create an PS3 account before you can buy games, this requires activation through a valid e-mail account.
Once you've connected your PS3 up, and have your internet running, you can slide your cursor over to the Playstation Store. You can then page down to the sign-in screen, where you will create an account.
After your account is created, sign into the Playstation Store. Odds are very good you will have to patch before logging in. These patches really do add some very helpful changes to the PS3, so I recommend you get them.
Once in, the store it isn't very much different than any other online store. Move through the menus, selecting the things you want and sending them to the shopping cart. While not many games are free, there are many that are low cost. Once you are done getting what you want "Checkout" and the PS3 will walk you through giving it credit card info.
Once your games are purchased they will have to download. It is perfectly ok to play an offline game while you wait, the PS3 will download it in the background. OR you can just go away for a while, and use the power off setting on the far left of the main menu to download the games and then turn itself off when done.