in short
The shuttle is launched at such a time so that its initial orbit almost matches that of the ISS.
Initial OMS burn after meco circularises the orbit. So the shuttle doesnt return to Earth.
Shuttle at this point is travelling at a lower orbit than the ISS and so is travelling faster than the ISS, so at this point the Shuttle is chasing the ISS ... Catching up.
Gradually the shuttle slows its approach to the ISS by increasing its orbital altitude, matching the altitude of the ISS by performing the burns you are talking about. The shuttle also fine tunes it's orbital alignment with the ISS.
Thats how it gets in the vicinity.
MCC uplinks burn targets to the GPC'S with the PADS / numbers given to the astronauts as a reference. I'm not sure if the astronauts input these themselves or it is simply a reference for what MCC has sent up. If I find a decent link will post back mate.
Hope that helps.