I just performed the garage pairing on a few cars and it seemed to go smoothly after the first one.
If I recall the car has to be on for the whole process (maybe not the engine, but I think mine was on each time).
Clear anything that it has currently by holding the 1st and 3rd buttons on the rear-view mirror until the light on it blinks quickly.
Bring the wireless transmitter / door opener into the car. Press and hold the button on the mirror that you want to program. While holding that button in, press and hold the opener button on the transmitter until the light on the mirror starts blinking, then release all buttons.
With the car still on from performing Step 2, press the learn button on the garage door opener (the actual machine mounted to the ceiling). Don't hold it in, just tap it. Regardless of what its called, its going to be the most dominant button on the device (bright red on some). After you've tapped that button, run out into the car and press & hold the same button that you programmed earlier for the remote transmitter until you see the light on the mirror blink like it did earlier.
You should now be done. For the car to open the garage door, the car's ignition has to be on and you have to hold the button on the mirror for a couple seconds.
Step 3 is necessary for the "some garage door openers require additional configuration reference in the manual. I haven't seen a garage door opener in the US that didn't need this... and the language in the manual isn't exactly clear.
Its the remote clicker first, then the actual opener, both for the same button on the mirror (same process).