Superb! any chance of letting us know the settings on the camera please (pretty please! ) and I'll have another go!
First thing you need is a tripod, no reason to struggle doing it hand-held like I do. Doesn't need to be an expensive one, you can get them on ebay for a pound or two.
At night, to state the obvious, there is a lack of light! So, the objective is to let as much light into the lens as possible to get a decent image but not so much that the image is washed out with too much light.
The easyish way - On most decent cameras, there will be an S option - that means 'Shutter Priority' or, to put it another way, all you have to do is select the Shutter speed and the other settings will be made automatically by the camera. So, a bit of trial and error is needed. Set the shutter to, say, 1/10th sec, and then try and get the autofocus to lock on to something like a distant streetlamp to that the focus is set correctly. Take the shot and see how it comes out. Remember to press the shutter button down gently to avoid shaking the camera and causing blurriness.
Too dark? Reduce the shutter speed further, to maybe 1/5th of a sec - you're giving it more time to let light into the lens. If it's still too dark, reduce the shutter speed again. Once it reaches zero, it will start to register in seconds, 1 sec, 2 sec etc.
Too light? Too much light is being let into the lens, so increase the shutter speed and try again. If it was on 1/10th sec, try it on 1/20th sec etc.
Doing it manually (the not so easy way) - you need to alter the following 3 controls on your camera:
Shutter Speed ( usually shown as something like 1/100) - This one is trial and error but, at night, will probably need to be anything from 1/10th second to a several second exposure (to get those nice trail effects on car headlamps)
Aperture (usually shown as something like f/2.5) - this needs to be as low as your camera/lens will allow ideally (until you get the hang of night photography).
IS0 (usually shown as a figure like 100) - the higher the figure, the lighter the photo BUT also the grainier the photo becomes. So, it's a tradeoff.