Ah, so you've scaled back a bit.
Basically, you will buy 2 sided copper clad fiberglass, perhaps in different thicknesses.
Expose a pattern onto the boards, which determines where copper will remain.
Cure that pattern, then immerse the boards in a solution that removes the unexposed copper.
Remove the material over the remaining copper.
Drill holes to all connections from one side to the other.
"Plate" the holes to connect the 2 sides.
Apply a solder mask to prevent solder from shorting between traces and other traces, or copper planes.
Apply/print any labelling.
QA control all along the way, including electrical test for continuity and not shorts.
Cut the boards to shape.
This site goes thru the steps in more detailn for how a board is made, with videos too. You can find other similar data online.http://www.eurocircuits.com/index.php/making-a-pcb-eductional-movies
As to what the actual machines used are along each step, now that you know what to look for, you can search for them online.
Different machines can do different maximum size boards, and I imagine different machines are needed for a simple 2 layer board vs a 4-6-8-12-14-16 layer board, the larger ones used for computer boards and backplanes, often with blind and buried vias (vias that connect internally but do not go thru all layers).