Easy with a bit of practice, and looks awesome to everyone watching.
It seems to me that a docking computer would be the size of a pinhead and cost half a credit.
Actually I think automatic docking functionality would be default in any ship's standard flight computer software.
It seems rather silly and archaic to have dedicated hardware for such a trivial task.
I would hope that there was one or two dedicated computers for such a trivial task since if one failed, it would be catastrophic which is why there are redundancies built into modern aircraft, for instance even for such a mundane task as locating north, I believe that there are three compasses just in case something happens to one which is why the elite docking computer is so heavy and costs so much.