Getting your equipment ready

You will need a soldering iron, some solder, and a blob of fixative such as Blu-Tack for this. I tend to always use leaded solder, as I find that it melts quicker and gives a better solder joint than unleaded solder, but the choice is yours.

Plug your iron in and allow it to come up to temperature. Once your iron is hot enough, apply a little solder to the tip. This is known as tinning your tip, and it fills any imperfections in your iron's tip with solder. This gives a better transfer of heat between the tip of your iron and the components your are soldering.

Now, insert the header into the Pi Zero and turn it upside down so that it is resting on the header pins evenly across the length of the Pi Zero. Then, place a blob of Blu-Tack under the side of the Pi Zero opposite the header pins, just enough to hold it flat while you begin to solder the pins, as shown here:

Now, we can begin to solder the pins to the Pi Zero; we are aiming for a nice, conical solder joint that just covers the brass ring around the hole in the Pi Zero board and comes to a point at the top of the pin. Place the tip of your soldering iron so that it touches both the brass ring on the board and the metal of the pin you are soldering, but nothing else, as shown next. Leave it for a few seconds to heat both brass ring and pin, and then apply the solder to the joint. The solder should melt, and you should see it flow into the hole and cover the brass and the pin. After a few seconds, remove the solder, and then remove your iron. Leave the joint to cool for a few seconds, and then move on to the next.

I tend to work my way down one side of the header and then rotate the Pi and solder the other side. The following picture shows what a finished soldered header should look like: