My understanding of how it SHOULD be done, you need to figure out how that compares to how it is done, and what should be done to fix it - it is sketchy in the extreme to have it any way other than how it should be... Remember that the electrical code has been referred to the "Book of the Dead" because someone DIED from doing it differently than what is in the book... Pools are extra risky in that water makes shock risks worse...
For 110V you should have THREE wires running all the way from the main panel to the end equipment, such as the pump. In the US they are supposed to be Black, White and Green. (Other countries use other colors - standards are wonderful because we have so many to pick from....) Black should ALWAYS be "Hot" White should ALWAYS be "Neutral" and Green should ALWAYS be "Ground" NO other color should be used in the main wiring, and no wire should be used for anything other than it's color. There is ONE exception, if using Romex to run power out to a fixture and back to the switch, you can use the white, for one side of the circuit, but the exposed white in the box should be covered with black tape in that case.
(Note that the electrons don't care what color wire they are running around in, but the color code is a requirement to make sure that the wiring is done properly)
The Neutral and Ground wires are tied together ONLY at the main panel, and should not be connected any where else in the system. They should also be free from ANY interuption - no switches in either!
The ground wire should have a pigtail connecting it to any metal box / fixture it passes through. (Note that unless clearly marked otherwise, you should NEVER put more than one wire under a screw terminal - if needing to connect multiple wires, use an appropriate size wire nut and a pigtail to the screw)
The Hot (black) wire should go from a GFCI outlet to the time switch switched contacts (in and out) and from there to the pump. Most codes say that the circuit should be dedicated, with nothing on it but the pump, the time switch clock, and maybe an SWG. Any auxilary function outlets should be separately wired, again with their own GFCI protection.
The GFCI breaker will have both the hot and neutral wires connected to it, and a pigtail running from the breaker to the neutral busbar in the panel. This is critical to get right - the way a GFCI works is based on the electrical law that the current in a circuit should be the same everywhere - the GFCI compares the current going out on the hot wire, and coming back on the neutral - if things are working right, the two will be identical. However if any current is leaving the circuit (i.e. going through your body to ground) the amount coming back will be different and the GFCI will trip....
If connecting things like outlets and plugs, motors, etc. the screws are also color coded - sort of... The neutral screw will be silver plated, the hot screw will be brass (or sometimes black) and the ground screw will be green....
Most GFCI breakers and outlets will have a "test" button on them - I don't totally trust this as it doesn't verify the downstream wiring. You can buy for a few dollars an 'outlet checker" which has three LEd's on it that will all light up if everything is wired right, and the good ones will also have a "GFCI test" button on them, which I prefer as it gives a true "end-to-end" test that is as close to simulating a real problem as you can get. I have made a short pig-tail adapter that I can use with motors and other fittings to verify the wiring by hooking it up temporarily to let me check....
(Note that I'm not a licensed electrician, but I do my own work with a code book in one hand....)
ex-Gooserider