Hi, and welcome to Shuttertalk!
For that type of photo, you need a lit and moving subject, long shutter speed, and a steady camera support. A tripods is best, but you may also be able to brace the camera on a railing or other sturdy object.
I took this photo yesterday with my Canon Elph (aka Ixus) S400, and the controls on your camera look essentially identical. They produce really nice photos, but sometimes you need to outsmart them. Mine was taken by setting the ISO to 50, its lowest, and zooming out for the maximum aperture. These combined to give a 1-second shutter speed, which was enough to streak the lights in the subway tunnel. The camera was held firmly against the window.
The other option for long shutter speeds is to manually set them. They need to be enabled in the setup menu, and then they're set through the EV (exposure compensation) function. You can choose 1 to 15 seconds, and then have to try it out to see what the resulting exposure looks like. It's trial and error, but this type of photograph suits it. Don't delete your "misses" until you get home and can play with them on your computer. Sometimes, the photos you weren't looking for can be the best ones.