I've taken alot of night shots with a variety of Sony cameras, ranging from ultra-compact pocket cams to ultrazooms to DSLRs. The good news is - even a compact like your W7 can take nice night shots.
As mentioned by most above, the tripod, or a flat, level surface, are the most important factor. If you don't want to buy a tripod for a compact, don't worry too much at Disney - there are plenty of garbage cans, posts, fences, walls, etc you can use to lay your camera down and keep it steady.
If you want the absolute most simple method - for true beginner-league stuff, try this:
First off - you are best to set the ISO as low as possible...ISO100 is usually best, as it introduces the last amount of noise. This is usually accessible in the primary menu - usually the first screen that opens when you press 'menu'. Scroll up or down as needed to find ISO. I believe your camera will have a choise of Auto, 100, 200, and 400.
Second - on the top dial, set the camera to the icon that looks like a moon. This is Night Scene mode. It will default to as long a shutter speed as necessary to get the shot properly metered.
Third - place the camera on a level surface, and set the self-timer. Aim, press the shutter button, and HANDS OFF! Let the self timer take the shot.
That's it! You'll get quite nice results with this technique.
As you gain a little more confidence, you may find you can tune the shot more to your liking by switching to S mode or M mode, and setting the shutter speed to whatever length of time you want. For example, maybe you are taking a shot in Tomorrowland, and you use the Night Scene mode. It chooses a 5-second shutter speed, and gives you a nice night scene:
It looks like nighttime, darker, and lights are muted and realistic to what they look like to the eye.
But say you want the shot to be more bright, more fantasylike, more surreal. If you were to use a longer shutter speed...the amount of light picked up by the sensor is significantly more, and therefore the scene will look much brighter and more colorful. Here is a shot fromt he same time of night, but at 20 seconds:
Shutters work like your eyelids - the longer you open them, the more you see. If you were standing at the Tomorrowland gateway with your eyes closed, and were to open them for 2 seconds...you might just get some of the highlights in your memory - the Tomorrowland sign lit up, the globe overhead, and some lights in the background would stand out but probably not the shapes or materials of the buildings. But if you were to open your eyes for 20 seconds...you have plenty of time to pull in all the details, for your pupils to adjust to the dark where you can see the ground, the walls, and the structures around you.
When taking night shots, try to keep that in mind. The longer the exposure, the longer the sensor is 'seeing' the scene, therefore the lighter and brighter the scene will be when captured.
Of course, there is another factor, which is the aperture (represented by the F number)...the aperture is to the camera what your pupil is to your eye. It makes the opening of the lens either bigger or smaller to let in more light or less light. So you also have the ability to go with a longer shutter speed, but close the aperture more, to end up with roughly the same exposure as you got with a shorter shutter speed but more open aperture. Confusing, yes!? It gets worse, when you learn that a bigger F number means a SMALLER aperture! Your camera may range from F2.8 (wide open) to F8 (smallest).
There is a reason photographers manipulate these two settings all the time, as aperture settings will alter the properties of the shot. Consider what a 2 second exposure with a wide open aperture of a highway at night would look like...in 2 seconds, how far would each car taillight or headlight in the shot have traveled? So your shot may have 2-inch-long broken streaks of light following the cars, but everything properly exposed and not too bright. If you were to simply increase the shutter speed to 30 seconds and leave the aperture where it is, there will be far too much light coming into the sensor and you'll end up with a big, white, blown out shot which is badly overexposed. So you have to close down the aperture in order to increase the shutter speed, and still achieve the same exposure. Get it right, and you can have a shot with the same proper exposure as before, but now the car taillights and headlights have streaked through your shot for 30 seconds, making them all merge into long, ribbony lines of red and white...a neat effect!
Hope that hasn't confused you too much. As I said, you can always stick to the Moon Mode until you start to get a feel for it. S mode can be your next experimental mode, because you can set the shutter speed you want, and the camera will figure out the aperture needed to properly expose for that shutter length. And when you get the hang of it, switch to M mode and set them both yourself. Your camera is capable of taking shutter speeds for night shots all the way up to 30 seconds, which is quite long for a compact...so you've got a great ability to take really neat night shots. I strongly recommend leaving the ISO out of the equation - for night shots, always drop it down to the lowest possible setting...compact cameras like yours don't do very well at higher ISOs, and since yours can only go to ISO400 anyway, no use turning up the gain and getting grain and noise in your shot when you can use nice long shutter speeds instead.
Good luck!