Halogen light bulbs -- more properly called lamps because the construction differs from a true bulb -- may have any number of base types. The lamp base and how it fits into the socket determine how you remove the existing lamp to replace it with a new one. Most ceiling fixtures use lamps with bases that either push straight in or twist to lock into place.
Turn off the power to the light before attempting to change the lamps. Turning it off at the switch is fine unless someone might come by and flip the switch as you work. In this case, shut the power off at the circuit breaker.
Remove any cover on the light fixture that prevents you from accessing the lamps. This may require removing screws with a screwdriver or prying or twisting off a faceplate for recessed fixtures. Flush-mount or pendant down lights usually don't require this step.
Pull firmly on the lamp, but do not yank. If the lamp comes out, you have a simple pin base. If you are using halogen flood lamps and there is no space to get your fingers around the lamp to remove it, you most likely have a twist-type base.
Push the lamp deeper into the socket if it doesn't come out when you pull. Use both thumbs to give even pressure to the lamp.
Twist the lamp counterclockwise while continually pressing inward. Release the lamp when it will no longer turn. It should pop out of the socket.
Replace the lamp using the opposite motion you used to extract it. Line up twist-style lamps with the widest openings in the socket, then press them in and twist them clockwise until they stop turning.
Never touch a halogen lamp with your bare fingers. The oils on your skin will cause the lamp glass to heat unevenly when it is turned on, causing the lamp to explode or burn out faster than it should. Cover the glass with a clean cloth or the lamp's plastic packaging materials as you install it.