How do I get 120 from a 3 way switch to wire a single switch

A one phase 3 wire system has a center tap. Two hots and a neutral. Typical 120/240 volts.
A three phase 4 wire system has Three hots in a Y or Delta. The Y system has three hots and the neutral comes from the center of the Y, this is the neutral and grounded conductor, 120 volts from hot to ground and 208 volts hot to hot. In a 3 phase system the voltage is not doubled hot to hot as in a single phase system because the hots are 120 degrees phased from each other and the square root of 3 is the factor, multiply the 120 volts by 1.73 to get 208 volts hot to hot. Multiply 208 by the reciprocal of 1.73 and get 120 volts. Your exact application is not given so it is not known. A delta system is a triangle and the angle of each triangle is a hot wire, one angle would be grounded or the center tap of one of the sides of the triangle. Y is the configuration of the windings of the alternator or transformer and Delta is the configuration as a triangle of the windings of the alternator or transformer where the power supply is.

With a three phase home service, you can only connect two hots from your single phase generator, and the neutral. One of the house's hot does not get connected and any three phase loads in the house should be switched off and kept from energyzing or a circuit breaker or fuse serving that 3 phase load may trip.
Only one power supply can be connected at a time. The power company power must not be connected at all while using an alternate power supply unless your power supply has means to synchronize the alternating cycle.

It is adviced that the loads be kept within 10% of their rated voltage, especially motors.

Load and line wires are reversed
http://waterheatertimer.org/GE-timers-and-manuals.html#15306
http://waterheatertimer.org/images/GE-15306-wiring-250.jpg
Switch wire on terminals L-1 with wire on terminal 2
Gene

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You didn't say what type compressor you have and didn't say what voltage.
A 220 volt compressor should use a double pole switch .
A 120 volt compressor only needs a single pole switch'
how to wire pressure switch for compressor YouTube

Single pole switch?
http://waterheatertimer.org/How-to-wire-switches.html

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208 Volt 2-wire is generally achieved by pulling two hot wires off 3-phase 120/208 Wye or 208 Delta, or Highleg to center tap off high leg delta.
http://waterheatertimer.org/How-to-wire-3-phase-electric.html
http://waterheatertimer.org/images/3-phase-timer-diagram3-T104-208-240.jpg

Since each of these three phase systems also offers 120volt for lights, and a dimmer can be used for lights, then I wonder what you are using dimmer for?

208 volts.can be controlled by turning off one hot of the two hot wires.
Install dimmer on one of the hot wires, and see what happens.
Is the dimmer rated for 208 volts?

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Un-plug the compressor and remove the cover to the pressure switch. Inspect wire connections for burned /discolored wires. If not burned, look for button to manually trip switch (switch has on /off lever, place in on position). Test with ohm meter for continuity. Switch is normally closed and contacts are usually visable to evaluate condition. Some compressors use a very small sealed pressure switch that is also normally closed.

11-21-12
Copy following links to identify timer and wiring:
http://waterheatertimer.org/GE-timers-and-manuals.html
http://waterheatertimer.org/Intermatic-timers-and-manuals.html#GM
http://waterheatertimer.org/Boxtype.html

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Get an electrician to do this. You don't want shock anyone in the pool!

Yes, the timer motor is 120 volt, so connect both neutrals from each separate 120 volt circuit to the "A" terminal. Probably best to place all the neutrals (line and load) under a wirenut with a jumper going to the "A" terminal. The terminals are intended for only two wires.
One hot will go to terminal #1 and the other will go to terminal #3. The 120 volt timer motor is connected internally at the factory to the "A" terminal and terminal #1.

The wiring diagram for that timer is somewhat misleading. The 120 volt clock timer motor is connected internally to the "A" (neutral) terminal and the #3 terminal. The "A" (neutral) terminal is to the immediate left of the #1 terminal.
Here's how to do the wiring for your use, (assuming a 120 volt supply circuit and a 120 volt lighting or other load):
Connect the incoming power (line) black wire to terminal # 3. Connect the incoming (neutral) white wire to terminal "A".
Connect the outgoing (load) black wire to terminal # 4.
Connect the outgoing (neutral) white wire to terminal "A".