We've been doing this a lot this week (and several stages are much easier with our new arbor press, I will say). The number one easiest way to get a pinion off a motor shaft is with a purpose-made
pinion puller. Basically, there's an outer structure which goes under the pinion and around the shaft, and then there's a thick pin attached to a screw mechanism that pushes against the shaft. The pin is slightly smaller than the shaft, so it pushes through the pinion and all the way out (in theory). This week, we found that our pinion puller had been broken at some point, so I used the screw part of the puller in the arbor press and cut a groove in a thin steel bar to hold the bottom of the pinion. Worked pretty well. However, some of our pinions were too close in to the motor, so we had to, uh, "finesse" them off a bit with a flathead screwdriver and a hammer to get enough space to put them in the custom puller.
Getting a pinion onto the shaft can be interesting. The only way I've done it so far is to use a vice with a plate that is thinner than the distance between the motor terminals so one plate pushes on the back of the shaft, and the other plate pushes on the pinion. That'll get you all the way until the pinion is level with the shaft. You can then use either pliers that are slightly open or some kind of metal tubing to push the pinion on the rest of the way. Remember to always leave space between the motor and the pinion, otherwise it will rub, and you will never be able to get it off.
The arbor press method would probably be the same, except you lay the pinion on the table (with the size disk removed), and push the motor shaft into it (with the motor upside down) with the bar on the arbor press. I cannot account for the "correct" way as to do this, but this will work if you're lined up COMPLETELY straight, and it shouldn't break anything.