Unplug a fountain pump from the receptacle or turn off the breaker for a hard-wired pump.
Add several drops of food coloring to the fountain basin and mix it into the water.
Examine the underside of the basin while wiping it with a white washcloth along the seams. Look at the washcloth for colored water to determine where the leaks are located. Wipe the washcloth around the bottom center of the basin where the pump wires run through fountain's vertical tube to observe for leaks.
Lift a removable basin off the fountain base and look at the seal. If the seal is broken, replace it with a new one.
Tip the fountain basin to one side and empty the water. Sand all of the cracks in the basin that you located with fine grit sandpaper. Put on latex gloves and apply epoxy to each crack, then smooth it with a fingertip. Allow the epoxy to dry according to the package directions, sand the epoxy with fine grit sandpaper, then refill the fountain and turn the power supply on.