It is done with a double side PCB. But if you are etching it yourself, you have to make sure you have connections only on the Top layer and nothing on the Bottom Layer at the header pins that go under the board. And you need to have connections only on the Bottom Layer for the pins that go on top of the board. Why? Because you can't solder under the pins and under the IC sockets. You ca do that for a resistor, maybe for a capacitor, or LED, or transistor, so these parts can be soldered on both sides of the board. If you need to use Vias, use a 0.5mm drill bit for them and place a (wrapping) wire through the hole and solder it on both sides of the board.
If you have the board made professionally, they will make the holes metalized, so the solder will flow through the hole on both sides of the board.