To R&R the pump, you need to pull the pulley off the old one to get the pump off the housing, then you need to re-install it using an P/S pulley installation kit, and you have to install it not too far or belt alignment won't be right.
Many times the pump will come with flush instructions. You need to block the return and put the return line to a fluid container. Start the car and have someone pour in P/S fluid as you turn the wheel lock to lock. Get a gallon of P/S fluid, maby more, you will use all of it in a turn or two. You might want to replace the lines while you are there. Sometimes they whine because of the pressure buildup from a clogged line.
Even after a flush, it may still whine some until all the air gets out. People struggle turning the wheel lock to lock, sometimes this works but many times it prolongs the problem by making lots of tiny bubbles. Just drive it, the air will bleed out.