Usually, when you're taking photographs in low light situations you can use flash, which can often leave your subject looking like a rabbit in head lights as they'll be very bright while the background is dark. Or the other option is to not use flash and slow your shutter speed down. This method's fine for photographing still objects but when it comes to people, unless you're photographing someone who's a musical statues champion, it's very unlikely they'll be able to stand still while the exposure finishes and as a result you'll get motion blur in the shot. Of course your other option is to use both of them together and on many cameras this function's called slow sync flash.
On compact cameras slow sync flash is often known as night mode and you can't control the speed of the shutter or the strength of the flash but you can with a DSLR. If you're working with a DSLR you'll find you have two options to pick from when working with slow sync flash and that's rear curtain sync and front curtain sync. Which one you choose will alter when the flash is fired during the exposure and as a result your images will appear differently. Rear curtain will fire the flash at the end of the exposure while front curtain does the opposite and fires the flash at the beginning. Rear curtain sync is great for adding impact to an action shot as when your subject moves through the scene they'll blur but the pop of flash at the end will leave them crisp and sharp.
As you're using slow shutter speeds a tripod is generally recommended. However, working hand-held when working with rear or front curtain sync can create interesting backgrounds for your images. It works particularly well where there's lots of lights as the flash will freeze your subject in place while the long exposure will blur the lights into an interesting mix of colour. If you're trying to create a sense of speed to make your subject stand out, photograph them against a dark background to reduce the effect of the flash.
What shutter speed you use will depend on the amount of blur you want to include in your image. So you need to experiment with your shutter speeds to find out what works for you.
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