To clean a mirror effectively you should first use a little rubbing alcohol and a soft cloth to get rid of stubborn debris such as toothpaste or hairspray.
Then spray a glass cleaner onto your mirror and use a microfiber cloth to wipe down the surface.
Work from the edge of one side of the mirror to the other side and then from top to bottom.
Avoid using a circular motion as this can leave streaks.
To ensure a mirror is streak-free, trying looking at it from different angles and at different distances.