In dimly lit places (without using the flash), you will need to use a high ISO (at least 1600) and a fast lens. If you had a dSLR camera (which has a large image sensor) and a fast lens (one with a wide constant aperture) shooting in a dimly lit place is not too much of a challenge.
The SX10 IS however, is a point & shoot type camera with a very small image sensor, which means it has poor ISO capability (no more than ISO 200...or 400, if you don't mind lots of noise). It's low light, ISO 800 and 1600 results are poor and only barely ok for small prints.
Your lens is fastest (f/2.8) at it's widest focal length of 28mm, but becomes much slower as you zoom in. You will not be able to handhold your camera using a slow lens and a low ISO. Luckily, you do have IS (image stabilization) which allows you to shoot with a faster shutter speed. But, for the best image quality, you will have to mount your camera on a tripod or sit it on a steady surface, use an ISO of 80 or 100 for the least amount of noise, select a slow (longer) shutter speed and set the timer. If you use Av (aperture priority) to set your aperture, the camera will select the appropriate shutter speed according to how much light there is. Or, you can set your aperture AND shutter speed (Tv) by selecting M (Manual) on the mode dial. However, in very low light make sure you're not zoomed in too much. If using a tripod, you don't need IS.
good luck, try a few settings to see which give the best results. That's the advantage of digital...