Summarize:

Climb up a ladder and take a close look at the ceiling light's shade to see what connects it to the base. Most shades are held in place by a couple of screws. Cup the shade, then use your free hand to turn the screws counterclockwise until the shade falls off the base. Then, turn the light bulbs counterclockwise until they pop out of the sockets. Some ceiling lights are held in place by tabs, which you nudge to the side to detach the shade. Check the owner's manual for your ceiling light if you have it. It will tell you exactly what you need to do to remove the shade. Alternatively, try searching for the make and model online for advice. Locate the screws holding the old fixture in place. They will be around the center part of the fixture, underneath the lightbulbs. Light fixtures typically have 2 of them. Twist them counterclockwise by hand and be prepared for the old base to fall off once they are loosened. Many bases are held in place by nuts on the screws. You twist the nuts counterclockwise by hand like you would with a bare screw. The base will slide off the screws as soon as the nuts are gone. Have a friend ready to assist you with the base so it doesn't fall. If you're working alone, try using painter's tape to loosely secure the base to the ceiling. If the base starts falling, the tape will catch it and hold it in place while you work on the electrical wires. Underneath the base, you will see the electrical circuit tucked into a junction box. It may look like a mess, but it isn't as complicated as it seems. The wires in the ceiling will be joined to the old ceiling light's wires, connected by colorful wire connectors that resemble caps on felt-tipped markers. Twist the caps counterclockwise by hand until you are able to slide them off of the wires. Before loosening the wires, consider taking a picture of them so you know exactly how you need to connect the new light. A basic voltage detector looks like a pen. To use it, press the "On" button, then touch the pen's tip to the exposed ends of the wires. If the pen lights up, the wires have an electrical current in them and are unsafe to touch. Voltage detectors are available online or at many hardware stores. Test the voltage detector on a circuit you know is turned on to check if the detector is working correctly. The voltage detector is a precaution to make sure the electricity is completely deactivated before you touch the wires. If the wires are electrified, check the light switch and circuit breaker again to deactivate them. Hold the wires running towards the light while you untangle them from the protruding wires with your other hand. When you disconnect the wires, the light fixture will be completely detached from the ceiling, so be ready for it. Pass it off to a friend or carry it down the ladder yourself.
Remove the shade and bulb using the fasteners on the base. Unscrew the base of the old light from the ceiling by hand. Twist the wire caps off of the electrical wires. Test the exposed wires by touching them with a voltage detector. Untwist the wires to disconnect the old light fixture.