Start by turning off the power to the existing light fixture at the circuit breaker or fuse. Verify that power is off using a neon circuit tester. Only then is it safe to remove the light fixture.
Working with electricity can be dangerous. Even less current than it takes to light a 60-watt bulb can be lethal. Always follow these safety precautions.
All wiring should conform to local electrical codes as well as to the current National Electrical Code (NEC). You can probably find a copy of the NEC at your local library.
Never trust a light switch to render a fixture "dead." Sometimes the power enters at the fixture even when the switch is located in the circuit beyond it.
Turn off the circuit you're working on by switching off a circuit breaker or by unscrewing a fuse (the house main switch should be off when handling fuses). Then padlock the panel if you can.
Make sure the circuit is truly "dead" before touching any wires or terminals. Check with a high-voltage neon tester. Test from the black wires to a grounded metal box or other good ground, then to the white wires. Also test from the white wires to a ground. Since there may be more than one circuit inside an outlet box, see that all of its circuits are off before you take off a cover. Also, be sure your tester is functioning by first trying it in a live receptacle.
Test your finished work with the power on using the neon tester. Check black to white and black to a ground. It should light. Test white to ground. It should not light.
If you aren't knowledgeable about working around electricity, call a professional.
A ladder will help you reach the light fixture. Using a cordless drill/screwdriver, remove the screws holding the fixture to the ceiling. Carefully lower the fixture, disconnecting the wires from the junction box.