How does the diameter of the wheel affect the speed of the vehicle?

Tire diameter has a direct effect on the vehicle's gearing/acceleration. A taller tire will act like a taller/lower numerical gear compared to stock.

An example of this..

A car with 26" tires, in direct 1:1, 3.0 rear gear will go 60mph at 2326rpms. The same car with 30" tires will be going 69.2mph at the same 2326rpms.

Depends on the engine and vehicle aerodynamics. If the engine has power to spare (when the engine's rpms are able to climb above where peak hp occurs) then a bigger diameter drive wheel will make the vehicle faster. This vehicle was redline limited, it didn't have the proper gearing to acheive it top potential. If the engine already have troubles getting to high revs then a bigger wheel will make it bog down and lose speed instead.

Smaller wheels will act as a lower gear, making the vehicle accelerate faster, but maybe not reaching the same top speed.