If you are saving money in a savings account at your bank, there is no reason why that money should not be earning you interest. Not all savings accounts, however, pay interest. A savings account may not pay the best return on your investment, but it a safe way to earn interest, as each depositor is insured by the FDIC up to $250,000. If you are not getting interest on your savings, it's time to put your money to work.
Shop around and find a bank that is offering interest on savings account and note the rate. Get a few different offers, as there is more to consider than just a high interest rate.
Check the fine print. Along with the interest rate, there may be requirements for minimum balances, number of transactions, fees or other charges that make a particular banks a poor option.
Apply these findings to your personal circumstances and eliminate the banks that won't work for you (for instance, if you would prefer not to deal with a minimum balance requirement).
Make sure the bank you choose is insured by the FDIC. The logo should be prominently displayed at the bank or online site. If you have questions, ask the bank directly.
Once you have made your decision, move your money into the account and begin to draw interest.