I know I earned dividends on an investment, but I did not receive a 1099. How should I go about figuring out how much income to report?

Make sure the dividends are not earned on an investment in an IRA account or tax deferred account. If that is the case the dividends should not be reported. Assuming the dividends are earned on a regular account try to contact the institution and request a duplicate 1099. If that is not possible, calculate the interest earned based on the statements that you have available.