First check the power rating of your soldering machine. That controller can only work with heating elements up to about 750W, if your heater requires more power you will have to use an additional relay or SSR to increase it's switching capacity.
Connections:
1. link pin 2 to the existing AC mains neutral and one side of the heater element. Neutral probably goes there already.
2. link pin 3 to pin 8 and to the line (live) of the AC mains.
3. link pin 6 to the other side of the heating element.
If you use a thermocouple, connect it across pins 15 and 16. If possible, do not extend the thermocouple wires unless you have identical wires to do it. Using ordinary copper wire will result in temperature errors.
If you find the unit works in reverse, off when it should be on, on when it should be off, swap the connection on pin 8 to pin 7.
Brian.