The moon is illuminated by the sun even when it's night time for the photographer, so it's brighter than you might think. Best thing is to not try to get a photo of the moon alone in a dark sky, but to frame the rising moon with something in the foreground that's illuminated. Lights on buildings, illuminated windows, traffic lights, a city skyline, etc. If you have the moon AND something terrestrial both illuminated, it can create a more interesting picture.
If you're using the camera you've talked about before, you have a Canon Powershot sx740 HS. It has a 4.3-172mm lens, but a very small sensor, so that is equivalent to a 24–960mm lens on a full frame camera (but without the quality and resolution you get from a full frame sensor). So you have a long telephoto lens when you zoom to the maximum.
Use manual settings and a tripod as both
@mollyc and
@kenoh said. Try to shoot just as the moon is rising, and not later in the evening. That increases your odds of having better illumination on foreground objects and a little of what we call "blue hour" sky. Also the moon appears larger when it's just above the horizon than later at night when it's above you in the sky.