The first place to look for that kind of information is NASA's Technical Reports Server.
I did some searching there, but I found no high-level overview. There's lots of detailed information, e.g. this report on acoustic models.
So your starting point may have to be something like the Wikipedia article on launch pads, and look up the more detailed info in the NTRS.
A Web search for "Launch pad design handbook" didn't turn up any results either.
Many aspects of launch pad design depend on the rocket you want to launch. E.g.:
- for a large launcher, you may need a water deluge system to protect the pad. for small launchers this is not necessary
- the rocket propellants determine what fueling facilities you need on the pad: which propellants and how much of each. Locations of the fueling ports on the rocket (at ground level or high up). Cryogenic fuels or storable propellants. etc.
- the preparation process for the rocket determines which facilities you need on the pad. The Shuttle launch pads were really elaborate, with a structure that allowed access to the payload bay so satellites could be loaded into the bay while the stack sat on the pad. Others are much simpler. If a rocket has to be integrated while vertical, you need a tall building next to the pad, and means to either move the rocket while it's vertical or move the building.