Here's a map so you can see what pin leads to what switch. Connect the switches of the 2nd controller to the 1st in Parallel, not series (that would mean both switches need to be pressed (AND))
https://cdn.instructables.com/FWD/RHYG/ ... MEDIUM.jpg
If you aren't used to soldering, i recommend you buy a bundle of through-hole resistors (cheap) and start practicing soldering them to a
stripboard (also cheap). That will boost your confidence and make your hand sure.
Your soldering station normally comes with care and use instructions. My thumb of rule is the minimal amount of time to get the solder point properly wet. Keeping the tip of the iron slightly wet at all times helps. I remove excess solder and possibly slag from the tip on a moist sponge between soldering joints. Just feed a little more solder as you hold the tip to the hole. You want the ring of the hole to be a bit warmed up before you apply solder, so that it bonds. This takes just a fraction of a second, though.
Here's a few illustrative pictures if you got it right or wrong:
