Cut power to the existing fixture at the breaker. Check to see if there is still electricity flowing by using a circuit tester and flipping the wall switch on and off.
Connect the white wire in the ceiling to the white wire on the fixture by twisting the ends and then screwing on a wire nut. Repeat the process with the black wires and with the ground wires if you have them.
Position the new fixture over the screws on the mounting bracket, and secure using the nuts provided.
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Release the fixture by unscrewing the nuts on its housing, and disconnect the hot black and neutral white wires coming out of the metal box in the ceiling from those on the fixture. You may also need to disconnect a third ground wire (usually green or bare copper).
Install a crossbar mounting bracket (kits are available at lighting supply stores), using the hardware provided.
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Turn the power back on at the breaker, and flip the switch on your new light.