> Can anyone shed some light on the complexity of installing a pump,
> maybe any advice on the process or a few tips?

I used to own a 2001 Civic but since I sold it when it was less than 2yo I
didn't spent much time under the hood.
First of all, are you relly sure that it is the pump that failed? Seems a
rather early failure.
Changing the pump shouldn't be very difficult. The complexity would only
vary depending where it is located and how easy it is to access.
Also how are the belts distributed i.e. how many belts and what is on which?
if you have AC? Depending on cars, you might need to remove another belt
(alternator and/or AC) to get to the power steering one. Then it should be
only 2 bolts to loose the pump and remove the belt and 2 hoses. I never
changed the pump, only the belt so I don't know how to bleed the system when
you connect the new pump. The manual should have instructions. Then it is
just the matter of putting the belts back (it might be worth replacing the
accessory belts at the same time) and set the correct tension.

As for the manual, make sure you can print out the pages you need as you
don't want to spend your day walking to the computer every time you need
some more information.