Via is something the PCB maker adds to the board to connect the layers. It is an extra step. The PCB maker will add copper inside the holes.
If you hand make this board, you will not have vias so you need to put a very short piece of wire in these holes and solder top and bottom side. Also, you will need to solder the top and bottom side on many of the IC pins.
If I did this board I would make the power and ground traces much widder. Add capacitors at all ICs and the transmiter power.