Hi PTDoc;
The contactor (relay) can be thought of as two separate circuits. The first is the load or "high current" circuit. The second is the control or "low current" circuit.
For the load circuit, you wire the contactor in just like it's a switch. The two hot wires go in one end, are switched on and off by the contactor and come out the other side. Just like Delta74 said, don't put the neutral (or ground for that matter) into the switch, it should never be disconnected. The three gang contactors are pretty common. If you get one, it will work just fine but you only need to use two gangs, just don't put any wires into the middle switch circuit, that won't hurt the contactor. Make sure to use a contactor rater in amperage as large or larger than the breaker controlling the circuit. Larger is just fine, smaller isn't. Also, the contactor needs to be rated to 240 volts AC.
For the control circuit, first make sure that you contactor "coil" is 120V AC. This means that the contactor is switched on an off by a 120V AC signal. There are many types of contactor coils. Some are 24V DC, some are 12V DC, some are 120V AC, some are 240V AC, some have an interchangeable coil. You get the idea, you are looking for 120V AC and that should be easy to find.
Now, you can think of the 120V AC contactor "coil" just like a light bulb and you can wire it that way and use any regular household 120V switch. When the coil has 120V applied (e.g. the switch is on) then the contactor will make the connection of the large wires and your compressor will operate. When there is no voltage applied (e.g. the switch is off) the contactor will not connect the large wires and the compresor won't work. There are contactors that are "on" until you apply voltage to the coil but they aren't as common. You will want a contactor that is "open" when the voltage is off.
Regarding the question of putting the contactor in a "three gang" box, I'm assuming you are thinking of a box with three "breaker" slots. If I'm correct in my assumption, than you can not do this. Those boxes are fom circuit breakers. Many contactors come in a box or you can get an empty electrical box and put it in yourself. If your switch is close to your compressor, why not just get a spa disconnect as some of us have suggested? The reason to do the contactor is so that you can put the switch far away from the compressor and have a "remote" switch for turning it on and off.
I hope this helps.