Am I to wire them together?
Yes well they won't wire them selves up.
Underneath the PCB or on top?
It is up to you.
What kind of wire should I use?
Again it is up to you and is not very critical.
I tend to use insulated stranded wire 10/001 - that is ten strands of 0.01 mm thick wire, but there are other types you can use.
As the board is just isolated pads it is very flexible. For example if you want to do a long run for say the power or ground then you can solder a length of tinned copper wire to the board to make a strip. I use 24 SWG wire for this. (SWG = Standard Wire Guage).
The skill is in only removing a short amount of insulation, from the wire. Tinning it, that is flooding it with solder. Trim it back, because the plastic shrinks back when the iron is applied, and then making a mechanical connection before soldering up the joint.
With only 40 or 50 years of practice you can reach the level shown on this project
Note I used solid core wire for that one.