I bought a similar board, can't remember quite where online I purchased it, but it was only like $5-$10. It came with an adapter that plugs in where the normal bulb goes and runs a wire to the circuit board.
This one works just fine, I didn't even attach it, just kind of stuck it in and put the dome-light cover back on. It slides around a little bit but not enough to cause much of a problem. It's much brighter than the original incandescent bulb