Removing the old primer pump is simply a matter of finding the proper wrench to either grab the flat sides at the base of the pump, or using a vice grip to grab the body of the pump. An offset wrench like pictured can be very helpful. Since the pump is being replaced it doesn't matter too much if the vice grips damage the pump.

Note that clearance can be a bit tight down by the primer due to fuel and power steering fluid lines in the area. However, if you're patient, you'll find a way to get the tools on and turn off the pump.

Note that there seems to be variation in the size of wrench these primer pumps take. The offset wrench I have is a 19mm which worked on a pump on another car, but was too small for this car. So I used vice grips.