Hi,
I do not understand how we know which part we need to program the micro when connecting with PK3.

As if I have one PIC18F87K22 and one PIK KIT 3, How do I know what other components will be required to program it, such as register capacitor,

 

VPP is on the master clear pin, put a 10k pull up on that (pin 9)

PGC (pin 52)
PGD (pin 47)

Be cautious of what you have on these nets, as that can affect the quality of the clock/data signals

 

How do I know what other components will be required to program it, such as register capacitor,

Just to program it you will need only the PK3 if the chip has an internal oscillator.
If it doesn't have internal oscillator then you will need an external clock source - see the datasheet for what is available.