Take multiple images of the same area of night withing a few hours. Line up the Stars in the image using software like Astrometrica. Objects moving within the solar system will stand out: planets, spacecraft and asteroids. If the object in question is not currently cataloged - it may be a new asteroid. Confirm your sighting on a second night. Send your position data to the IAU Minor Planet Center - if new it will receive a new designation. With modern computers, asteroid software and digital imaging - much of this work is now done within days and can be done by almost anyone interested in learning the techniques and tools.