Shooting at night is not easy, especially with a point and shoot camera. To get decent night shots, you need one of two things - a stopped train or your own source of light (which has to be very bright and last a very short period of time). The easiest option would be to set your camera up on a tripod and find a stopped train, and use either a remote trigger or the self-timer to trigger a long exposure - some trial and error will probably be involved to figure out what settings work best, and you'll want to keep the ISO low to avoid hot pixels creating noise.
The other option, having your own light source, is a lot more expensive, takes a lot longer to set up, and can be pretty difficult to do well, but it's my favorite way of doing things. I have five Nikon SB-24 speedlights, which each have a guide number of about 140. (Guide number - number of feet away to get a good exposure at F1.0 and ISO 100 - but more on this in a minute, and why you'll never be able to shoot something 140 feet away at ISO 100 with a speedlight, at least that's my understanding of it.). Other people use big monolights, like Alien Bees, and get great results with those too (and they put out a lot more light), but they're heavy, expensive, and generally require an external power source, which adds even more to the cost. With the speedlights like the SB24, I can generally light up a train/building between 40 and 60 feet away, although I have done one shot at about 90 feet away before. The reason you'll never get something lit 140 feet away is pretty simple - I only know of one lens that goes to F1.0, it's incredibly expensive, and there's no depth of field at F1.0 so it's next to impossible to focus especially at night. Generally, you'll want to use more moderate apertures, between F4 and F5.6, as this will give you better depth of field and most lenses tend to be sharper when stopped down. This will requre a higher ISO, but most modern DSLRs do fine at ISO 1600 and under.
Problem with off camera flash is that a point and shoot camera won't fire them. They don't have the jacks for the cords or a hot shoe to put remote triggers into, and let's be honest, point and shoot cameras suck at ISO 800 because of their small sensors, and you'll need at least ISO 800 to have the light carry well enough to light up a train. I use 1600 quite a bit and have done one shot at ISO 3200, although it came out pretty soft because of all the noise reduction I had to do. So to go the OCF route will be kind of expensive, but not as much as you might think. You can get fairly recent DSLR like a Nikon D3100 for under $200 now from KEH, and used 18-55 kit lenses are incredibly cheap now too, and surprisingly, decently sharp if you don't mind the plastic build and a few missing features. As far as the lights go, I paid $125 TOTAL for all five from KEH during a sale last year, and I use Yongnuo triggers, which ran me $100 total for all 6 tranceivers I needed to have one for each flash and one on the camera. It's entirely possible to get a decent start into off-camera flash for under $500.
Now that I've gotten light placement down pretty well (it involves a lot of learning through trial and error), the toughest thing for me is focusing. Sometimes I get enough power from a pocket flashlight to focus the camera, sometimes there's ambient light or a large object that's stationary near the rails to focus on, and sometimes, it's just guesses made with trial and error and using the (rather inaccurate) focus distance indicator on my Nikon 16-85mm lens. I still mess it up occasionally.
Anyway, here are a few of my examples, lit with the 5 SB24s, and I'll link to Kent Staubus's Flickr down below also. He's a friend of mine who taught me a lot about what I know about shooting at night. He started out with smaller speedlights but now uses Paul C Buff Monolights and does great work with them.
And Kent's Flickr -
https://www.flickr.com/photos/96826069@N00/