One thing that often stumps people as they get into taking pictures on a more serious level is how to deal with low light or night photography. They point their medium to high end compact at a beautiful scene, press the shutter, and are immediately disappointed with the results.This is because most compacts in auto mode don't support or at least won't choose long shutter speeds. Those that do support longer speeds often only allow them to be used in the 'semi automatic' or manual modes. If you turn on Auto ISO (The Devil) then problems are further compounded as the camera will crank up the sensitivity in order to get you a hand-holdable speed. Of course in this case we're not expecting a hand-holdable speed. Consider the attached shot.
This was shot at ISO 800, 1.6 seconds at f/4, on a 20mm lens. I've adjusted levels and done some slight sharpening in Photoshop 6.0 to get the best out of the medium JPEG because I didn't have the tools to hand to process the RAW file. Local time was around 11pm and the light was fading as we approached this bridge which connects the island containing Copenhagen with mainland Denmark. In a one-chance situation like this it's important to plan what you want to get and how to get it before the 'decisive moment' (as Henri Cartier Bresson would describe it) arrives and then is left in your wake, mocking you about having missed the shot. In my case I took a number of test shots before this, and came prepared with one of my favourite photographic accessories, the Pod, SLR edition. This is a squat cylindrical beanbag with a tripod thread at one side. It's perfect for propping the camera on a rail or similar and letting go for a second or two, when a proper tripod is either too bulky or just not available. What I normally do is set the camera on self timer with a short delay (2 seconds on my SLR) unless I have a remote release to hand, prop it in place, push the shutter, then let go entirely, hovering my hands around the camera until the shutter opens and closes. This allows me much more freedom to use longer speeds than would otherwise be possible.
In terms of hand-holdable speeds the rule of thumb has always been the reciprocal of the focal length (i.e. for a 20mm lens, 1/20sec). Modern cameras and lenses often include stabilisation which allows a couple of stops of leeway on that, so maybe 1/4 of a second or so. At that speed, given that my lens aperture was wide open I would have had to increase the ISO by three stops, to ISO 6400. Even if my camera supported that the quality would have been awful. Hence the pod.
I was therefore limited only by the 'environmental' features inherent in this shot - namely the motion of the ship and the crush of people around me. I therefore settled on a compromise of 1.6 seconds, boosted the ISO to 800, and let the aperture stay fully open, as the depth of field would be sufficient given the wide angle lens and the subject distance. More than 1.6 seconds caused visible movement in the bridge itself, and less would have required the use of ISO 1600, which was further than I wanted to push it.
In term of the remaining technicalities then, the camera was on evaluative metering which did a pretty good job with exposure (albeit a bit flat). This is what I'd recommend you try first if you have options. You may find that the whole scene turns out a little too light and lacking in contrast, in which case you can dial in a stop or two of exposure compensation to bring it down. Again, keep taking test shots until you're basically happy with the appearance and then you can concentrate on composition.
Many compact cameras will only go to these longer speeds if given no other choice so if you find your pictures being very dark and your shutter speeds hovering around the 1 second mark, try shutter priority if you have it and see whether you can force the speeds to go long.