It's the old catch-22. You cannot establish a credit history without having credit, and you cannot get credit without a credit history. But if you work at it, this problem can be overcome. While you create a history, be sure your efforts will be reported to the credit bureaus.
Use the credit history of a family member or friend to leverage yourself into credit in your own name. If you are added as a joint party or authorized user to another person's credit card, the lender may report the account's payment history on your credit report.
If you have a checking account, ask your bank for overdraft protection (or cash reserve) privileges. With this feature added to your account, you can create credit by writing a check for an amount greater than the balance in your account (but not greater than the limit of your cash reserve line!). Alternatively, ask the bank for a small personal loan. As you repay these debts, you establish a credit history. Make sure the bank reports that history to the credit bureaus.
Secured credit cards are also a good way to get started. Your credit line is secured by your deposit in the bank, minimizing the creditor's risk. For example, if you deposit $500 in the bank, you get a credit card with a maximum limit of $500. As you use the card and make payments, you establish a credit history. These cards have high interest rates, but your goal is only to charge what you can afford to repay. As you repay the debt, you establish a repayment pattern seen by other creditors.
You may also want to see if you qualify for a retail/department store charge card or gas card. Because these cards have lower credit limits and may be used only with the companies that issue them, the lending guidelines may be more liberal than those for major credit cards.
If you still have difficulty obtaining credit in your own name, consider a collateralized or cosigned loan. With a collateralized loan, the item you pledge as collateral (such as a car) minimizes the risk to the credit grantor. With a cosigned loan, your cosigner is equally liable for the balance. Spreading the responsibility for repayment in this fashion minimizes the lender's risk. Successful repayment of these types of loans can then be used to establish your own credit history.