These guys are doing a great job of explaining but let me throw my two cents in here.
As far as actuating the gear goes, the RG is pretty unique. Most retractables use a reversible pump. The RG pump only runs one way. Fluid is directed into either the pressure or return (up or down) lines by the selector valve which is rotated by the gear handle. If you look at the diagram in the POH with a magnifying glass, you will see how the selector valve rotates to align the fluid coming in from the pack with either the up or down lines. The lines not selected serve as the return side and the fluid flows around the valve, back to the pack.
Since the selector is not an electric switch, how does the pump know when to run? Simple. Anytime the pressure in the system drops below a certain level, the pump goes to work. As avbug said, anytime you move the selector, pressure bleeds down to almost zero, turning the pump on. The actuators move to full travel, pressure builds, pump turns off.
It is important to note that the pump will run if pressure is low, regardless of the position of the gear. Limit switches do not turn the pump off in the RG. The squat switch does, theoretically. Its position should be checked on every preflight and it should be open on the ground.
You asked how the squat switch works. OK, pressure switch gets the signal that it's time to run the pump. Sends signal through the squat switch to the pump. Squat switch open...pump no run. Closed...pump runneth.
There are many gear up incidents in the RG compared to Piper products and I'll tell you why. Most are inadvertent retractions on the ground. One, it's a trainer, so lots of touch and goes. Two, the squat switch is on the nose gear. If any lift exists during the roll, the nose gear is likely to not have much weight on it. If the gear handle is moved, it will retract. Also, any bumps on the runway/taxiway can lift weight off the nose. The squat switch on Pipers is on the mains. Hard to get weight off of those unless you're flying.
Now the downlocks. I believe they are forced down by springs and overcentering. The gear slides on the smooth side of the 'J' in the down direction and then they pop down, holding the gear in place. To retract the gear, the downlocks must be lifted up, allowing the gear to travel by them. On some planes this is accomplished mechanically but not the RG. The RG has small actuators solely for the downlocks. When gear is selected up, pressure travels not only to the 3 gear actuators but to 3 smaller actuators whose sole purpose in life is to pivot the downlocks up.
I believe the actuators now have an AD on them to be inspected frequently. Maybe even a dye test. Haven't flown it for a while but I would definitely check it out. Hard landings will crack the actuators and this will cause a situation where the gear will not extend/retract, even with the emerg. pump. Check em closely. This has caused many a bad day. If you see hydraulic fluid (red)under the airplane, DO NOT fly it.
