Here are a few ways you can start off:
Secured credit cards: If you make a security deposit of $300, you get a credit for $300
Department stores: Generally speaking, Khols, Macys, Sears and some other local chains have private labeled credit card programs that are easier to get approved than Mastercard or Visa.
Get a card with a co-signer: If you have someone you truly trust (and of course truly trust you), get a credit card with you as a co-signer.
Once you get your credit, try to keep your balances no higher than 15% of the limits.
Below is the application for the secured card. That is your best way to start.