There's some YouTube videos on how to solder... For example this random one looks like the capacitor has been harvested and has very short leads: https://youtube.com/watch?v=iDtXq21bKYg
Basically: Get the polarity right, or it'll blow. Touch both the lead and the pad with your soldering iron, and after a second, add the tin solder, wait another like two seconds for it to melt and connect everything and you're done. Then check your work and see you didn't inadvertently short-circuit anything else. Shouldn't be too hard for a capacitor as the pads are quite far apart. And don't burn the capacitor by heating it up for way too long.
Pro-tip: Once you test the device, put the casing on to avoid touching mains voltage. Will also contain something like an exploding capacitor so you don't get it into your eyes. If it works you can tighten all the screws.