Plug in the fountain lights while the fountain is still full and experiment with several positions for them throughout the fountain. Try this at night as well to see the effect of the various potential positions. Determine which locations will be used and mark them with a discrete marking. Find the most convenient positioning for the exit of the light cord, which will sometimes be over the side of the fountain, through the central unit of the fountain or out through a hole that must be made in the bottom of the fountain.
Drain the fountain and allow time for the installation surfaces to dry. When the surfaces are dry to the touch, sand each marked area and wipe it clean. Smear a dollop of waterproof caulking on the spot. Push the light down into the caulking, adding extra if necessary for a complete seal. Repeat for the rest of the lights.
Drill a hole in the base of the fountain where the cord must exit, if necessary. Run the cable of the lighting out through the hole and fill the hole with waterproof caulking from both sides. Allow the caulking to dry overnight and then refill the fountain.