Install Headers to Pi Zero
The Raspberry Pi Zero ships with no headers installed on the GPIO. Insert the 2x20 (or two 1x20) headers into the GPIO like shown the photo. The black plastic bit should be on top of the PCB.
Tack Headers to PCB
Use tape or mounting tack to hold the header onto the PCB. Then, secure the PCB to a pair of Helping Third Hands or a Panavise Jr. This will make it easier to solder.
Flip the PCB over and solder all of the pins to the GPIO.