For this article, I am going to install a low profile LED light fixture on a ceiling fan. This was required as the ceiling in this house is quite low, and a standard fan light fixture would not fit.

Step 1: Safety

This is electrical work. Electricity can kill. You need a basic understanding of household wiring to complete this project. I highly recommend using a digital multimeter to find the proper wires, and make sure the power is off before touching any bare wires.

Step 2: Parts Used

The fan I used is an unknown brand that was installed by the previous homeowners.
I used a flush mount utility LED light from Home Depot, along with three 6-32x5/8" screws and nuts, and three brass 8-32x3/8" screws. The exact screws required by your fan/light combination may be different, please look your setup over before starting.
The switch is a single pole pull chain switch, with a 3/8" hole drilled through the lip of the light housing to fit it.
I also used a 5/32" drill bit to drill the holes in the closure cap of the existing fan, and a 3/8" bit for the switch hole and wiring hole.

Step 3: Find Power and Start Modifying

Standard US household wiring code calls for a black power wire and a white neutral, with green being ground. Pop the closure cap off the bottom of your fan and find the black and white wires. With the power on, check for 120v across these two wires, and make sure the voltage is constant regardless of the fan speed or direction. Once you do that, turn the power off and verify it is off by checking both between the two wires and between each wire and the ground (or metal housing if there isn't a green ground wire).
The mods to the light itself are fairly straightforward: The three screws that hold the LED panel to the light housing are replaced with the longer 6-32 screws one at a time. I pulled one screw, centered the light on the fan closure cap, and marked through the hole where to drill the cap. I then drilled the cap, installed the longer screw in the light, and used that to hold the cap in position while marking the next hole, and the same for the third. Once all three holes are drilled and the screws installed set the cap aside. Most of these caps can only be installed one way, so think about where you want the pull chain to be, then drill the hole and mount it. One black lead from the switch will be wired to the fan wiring, the other gets connected to the black lead coming out of the light using one of the wire nuts supplied with the light fixture. The white lead from the light gets connected to the fan wiring.
Tuck the excess wires into the rim of the light fixture and fix in place with a dab of hot glue.

Step 4: Fan Modifications

Once the light was modified, I went ahead and drilled the hole in the cap for the wiring to pass through, and used the 6-32 nuts to fasten the cap to the light. Mine was already drilled and tapped for 8-32 screws around the rim to hold it on the fan body, but the screws were missing so I got three brass ones to replace them.
Once the cap is attached to the light and the wiring is passed through the hole, it's ready to install.

Step 5: Installation and Test

Have someone hold the light fixture up for you while you connect the light into the fan wiring. On mine, I simply undid the wire nuts the fan already had, added the light wires to the wiring bundle, and put the nuts back on.
With the wiring complete, carefully put the light into position and install the cap mounting screws.
Turn the power back on and give the light a test. If it turns on and off, you're done. Now you can sit back and enjoy the benefits of upgraded lighting.