For the next few steps, I'll be referring to the "front" of the dome light as the part that is closest to the front of the car, and the "back" of the dome light as the part that is closest to the back of the car.

Pry one of the back corners away from the ceiling and use a plastic trim tool to pry the dome light downward from the metal pan it's clipped to.

Now pry the other back corner away from the metal pan the same way until the back of the light is hanging by the power plug.

Unplug the power cable and pull the dome light out toward the back of the car.

Remove the four screws and lift off the backing plate.

Here's a shot of the part number for the dome light, just in case you were wondering.

Unscrew the four screws holding each map light fixture in place.

Pop the map light fixture out of the frame.

Remove the two screws holding the map light fixture together.

Separate the back of the fixture from the front, revealing the bulb.

Use a skinny object to press the bulb out of the socket from the back of the fixture. (I'm holding it crooked in this picture, but you should press straight down through the hole.)

Repeat steps 4-6 for the other map light.

Carefully pry off the plastic cover from the bottom of the dome light, starting with each end.

Pry off the middle of the cover to reveal the dome light bulb.

Remove the dome light bulb the same way you did with the map light bulbs.

Plug the new bulbs into each fixture.

Plug the dome light back into the car to test out the bulbs. If you're using LED bulbs, they may not work the first time. If they don't, take them out of the sockets and turn them around the other way. LEDs are picky about which way they're inserted.

Now that you've tested the bulbs to make sure they work (you did that, right?), it's time to reassemble the whole thing.

Reassemble the map light fixtures. The bulbs I used were directional, and their shape interfered with the silver reflector that normally goes between both halves of the fixture. I decided to omit the silver reflectors when I reassembled the fixtures.

When you're reinserting the map light fixtures into their frames, make sure you line up the little nub with the trough in the frame. Failure to do this will result in map lights that don't pivot properly.

Press the front cover back onto the dome light. Start from one side of the middle, then do the other side, then work your way out.

Insert the two tabs into the front part of the hole first (the part closest to the front of the car).

Then, plug the fixture in and snap it back up into place. There's not much slack in the plug, so it might be tricky. I had to only put the right tab into the ceiling, plug in the light, then maneuver the left tab into the ceiling before pressing the whole thing back into place.

Enjoy your new bulbs! The LEDs I chose are daylight balanced and slightly brighter than the original incandescent bulbs.

Here's a comparison to the old bulb color.