Find out if your state allows you to file for extended unemployment benefits. Some states are cutting back on this, while others (like Michigan) have already eliminated it. This was done to prevent abuse and to encourage people to get back into the workforce faster. Few states now allow for extended benefits at any time. Most have an on-off policy, depending on the unemployment rate in the state.
Call your state's unemployment office to see if your state follows the "periods of high unemployment" rule. Under this rule, some states that experience particular economic crises or go through transition eras may allow for extended benefits (up to 13 extra weeks) so workers can keep searching for jobs.
Wait for an official notification. Once your regular unemployment benefits have run out, you should receive a note from your unemployment office alerting you to the option of extending your benefits. Until you get that, you will not be able to get any extended benefits. You can, however, confirm the existence of an extended-benefit rule in your state by contacting the unemployment office in advance.
Apply to get extended benefits by filing the appropriate forms (available from your unemployment office) and making sure you provide all of the extra required paperwork. Contact the same office where you originally applied for unemployment.
Apply for an appeal if you are denied extended benefits. You can do this directly through the unemployment office, or you can do it privately by hiring a lawyer to help you through the process. Appeals, however, can take a long time and be quite costly, so they only make sense if the amount you are set to receive is high.