After you remove the pulley (held on with the 3 small bolts) and get it wiggled off of the hub of the pump, then you can remove the pump from the engine accessory bracket. The -hub- is still on the p.s. pump shaft; Its what the pulley bolts to. It is a press-fit on the shaft. Unless you paid the higher price for a rebuilt/new pump having that hub on it, you will need to take the hub from your old one. I use a 3 jawed puller to do it. The end of the p.s. pump shaft is threaded inside. You need to fill that threaded hole with a bolt that matches the threads, (on mine it was something like a 5/16-18 bolt, not a metric size). This is so the screw-post of the puller has something to push against. I clamp the p.s. pump into my bench vise, turn the screw-post until its snug, then use a large & long screwdriver to hold the legs of the 3 jawed puller from turning. If you dont own a 3 jawed puller, you can probably rent one from a place like Autozone or Advanced Auto, etc.
Usually the new pump comes with a bolt and a nut. You put the nut onto the bolt and run it up near the head. Then you put a nice thick washer, then the hub, then you thread the bolt into the end of the shaft as far as it will go. Then the nut is used to draw the hub onto the shaft.
Sorry if I have been telling you the obvious, but other folks read these postings who may not know what you have to do to 'move' the hub to the new pump.
Of course you never ever hammer on the end of the p.s. pump shaft.
Anytime I am replacing a power steering pump, I make it a point to get some fluid into the pump, so the vanes inside it will be oiled when you first start the engine. Those vanes can get 'burnt' fairly quickly if they have to run 'dry'; and make the whining noise for thousands of miles.
If you dont own a pullery and go to buy one, I wouldnt advise buying an intexpensive one.