The one of first things you should do to building your own credit is get a paypal account. It is Free (except fee's they charge for transferring lager amounts of money, however purchasing stuff online is free).
You should have a checking account, I think you can get an account without one to receive money but it is a good idea to get or have one. If you do not have a checking account, you will have to apply for a paypal debt card but they are not given out like candy, it may be hard for people with poor or no credit.
Since Paypal is affiliated with GE MoneyBank it builds your credit when you buy stuff with your Paypal account. If you are not interested in building your credit, paying with a Paypal account protects your bank/credit card information, that alone is a good enough reason to open a Paypal account. Because of its safety features, it is a favorite of smaller online stores; they know people are more likely to buy from them if they accept Paypal.
Almost everyone online deals with Paypal. If you work online (do paid postings, sell ads on your blog, etc..) You can be paid a lot faster then if you waited for a check (that could bounce) and safer then if you direct deposited into your bank account.
Paypal also has Paypal Buyers Credit and a business credit card that you can apply for once you have built enough credit.