the switch works because when you fold the paper over it bends the copper over to touch the other piece of copper and complete the circuit. To solder you have to touch the soldering iron to the copper and hold it there. then you touch the solder next to the soldering iron. The solder should melt and create a shiny bump, then put the part you want to solder on the bump and press with the soldering iron.

this is an example of a good soldering joint