The way I built my credit history was with a secured Visa card. It's been a while and I don't have that credit card anymore or even remember what company it was but I do remember that I had placed $300 into their savings account and they gave me a credit card with a $300 limit. It didn't feel so good having to give all that money just to get a credit card in that amount but I didn't know any alternatives since I had no one to credit piggy-back with. It worked and years later I had built my credit score enough to get some of the better unsecured credit cards out there. By the way, I remember with that secured Visa you had to keep your $300 in their bank for two years. After that I requested my money back and they returned it to me plus a couple bucks extra interest.
If you don't want to go the secured credit card route then there are credit card companies that offer credit cards that are aimed for people to build a credit history. If you have not ever had any credit many see your credit the same as someone with bad credit so you are in the same boat. Do you have No Credit or Poor Credit? Find the right Credit Card for your situation! here. Another place you can check out is at Credit-Land.com - Find the best credit cards for your needs.