If you have an old light or other fixture positioned a few feet above your bathroom sink (a common configuration), why not switch out that dated thing for a modern lighted mirror? Any local home improvement store will offer a wide array of all-in-one units that contain a decorative mirror, multiple lights and sometimes a built-in medicine cabinet. And it's as easy to install as hooking up a single-bulb fixture.
Turn off power to the room at the fusebox. Remove the existing electrical fixture from the wall by taking out the screws and disconnecting the wiring.
Stand your new lighted mirror in front of the open electrical box on the wall, leaning the mirror back so you can work with the box.
Attach the wires from the box to the corresponding wires on the back of the mirror, holding the two wire ends next to each other and twisting a wire nut over both of them, then wrapping the connection in electrician's tape. Generally, there will be one black and one white wire coming out of the box, which needs to connect to the black and white wires on the back of the mirror.
If there is a bare copper grounding wire coming out of the electrical box, hook it around the green grounding screw on the electrical unit at the back of the mirror, and tighten the screw.
Mount the mirror and lighting unit on the wall according to the instructions it came with. In most cases, there will be a mounting bracket that screws onto the electrical box and then holds the mirror-and-lighting unit. Put in the light bulbs and turn on the power.
When buying your mirror-and-lighting unit, carefully consider the placement of the electrical box on your wall, as it will have to match the placement of the electrical unit on the back of the mirror. Generally, mirror-and-lighting units are designed to allow some flexibility on that issue.
Make sure the power to the room is off before you start your project.