I like to spray the shaft with WD40 or other penetrating lubricant before applying the force via the screw, some say it makes no difference, but I find it does seem to make the job easier once the parts start to separate.
Simply hook the arms of your gear puller behind the gear or bearing and adjust the arms so that they are evenly spaced either side of the centre screw and spin the screw down onto the end of the shaft. Once finger tight apply an even pressure with a spanner or socket to the large head of the centre screw. I find it easier to hold the puller in a vice (not the shaft, you’ll damage it) and then you have both hands free to hold the puller in place and turn the screw.
As you carefully turn the centre screw downwards it will get very tight as the force builds up until the pressure overcomes the friction or interference fit. Usually you’ll think it’s totally stuck and then with a little ‘bang’ it’ll start to move (this is where the WD40 helps). Keep winding gently until the gear or bearing pops off the end.
You might find that the arms are too big to tuck behind the bearing on a small job. Sometimes you can get out of trouble by grinding or filing away a little metal on the end of the arms, narrowing them a little to make them fit. Bear in mind they are under a lot of pressure though, so don’t go crazy here and grind them so thin they break.
If you’re removing a good bearing you want to keep, make sure you have a gear puller with arms deep enough to reach the inner bearing ‘race’ (the one on the shaft). if you put the arms on the outer ‘race’, you are applying a lot of force onto the ball bearings inside the bearing and it’s possible to ruin the bearing (if the bearing is scrap then of course it’s OK to pull the bearing off using the outer race).