Select a bit for your smaller, handheld router. You may want to practice setting up and using this type of bit before working on your cabinet.
Secure your piece of wood with a vice before cutting. If the cabinet door is made of several pieces of wood together, make sure they are glued and secure before cutting the edge of the door.
Hold the router steady and move it slowly, but firmly, around the edge in a counterclockwise motion around the door. If you are using your router on the inside of the door, such as in cutting a window out of the middle, rout it clockwise. This should help you avoid chipping out corners, according to The Family Handyman (thefamilyhandyman.com).
Sand the edges and examine them for imperfections.