Call your state unemployment office claims center to stop the claim if you have just recently applied and have not received your determination letter yet. Once you file a claim, the benefit year begins, which means if you become unemployed later in the year you must use the same claim instead of filing a new one. Stopping a claim before it is processed can prevent this from happening. The Job Hunt website (see Resources) has a listing of unemployment offices by state, if you do not have the contact information.
Throw away the next weekly claim form that you receive in the mail and do not file or certify for benefits. Failing to claim your weekly benefits automatically stops your unemployment benefits. The claim does remain open for the remainder of your benefit year period though. This means that you can restart the benefits at any time during that period.
Email your state unemployment office to let them know you resumed employment and are stopping your unemployment claim. This is not required in any state, but you can do so if you want to keep a record of it. Typically you can use the "Contact Us" option on the state unemployment website. The Job Hunt website (see Resources) has a listing of unemployment offices by state, if you do not have the contact information.