The key to photography is ensuring that the right amount of light hits your film and exposes the negative. Too little light and your pictures are underexposed (very dark) and too much light and your pictures are overexposed (too bright). Most cameras have accurate light meters that determine the correct settings to create properly exposed pictures, but these are only effective during daylight. Often at night the camera will be unsure of the settings to use and take underexposed pictures. This means that you need to do the thinking instead of your camera and choose the correct settings yourself. It may be intimidating at first, but practice makes perfect.
Note: All this applies to digital cameras the same as film cameras expect for reciprocity failure
When you change a camera setting, you are either doubling the amount of light entering the camera, or halving it. This basic relationship is called a stop. Stopping up means doubling the light in a picture while stopping down means halving the light in a picture.
There are three main ways that you can control the amount of light in a picture. They are:
Film speed is often the first choice you make when you take pictures. The type of film you use affects how sensitive it is to light. The film speed ISO numbers indicate how sensitive the film is. Each time the numbers double (going from ISO 400 to ISO 800) the film is becoming twice as sensitive to light. Each time the numbers half (going from ISO 200 to ISO 100) the film is becoming half as sensitive to light. This means that higher ISO numbers (800, 1600, 3200) are highly sensitive to light and the lower numbers (25, 50, 100) are not very sensitive.
Now for night photography, you might think that it would be best to shoot with the fastest film you can buy. The problem is that the higher your film speed is, the more grain (or noise for digital cameras) is in your picture. Low film speeds take very clear pictures, but require either long exposure times or bright conditions. Photography is all about trade offs.
The next way light is controlled is through the aperture. The aperture is a little hole in the lens that you can make bigger or smaller to allow more or less light to pass through. Aperture is measured using f/stops which is distance between your lens and film, measured in apertures. This is slightly confusing at first but remember that it is the aperture you are changing, not the distance between the film and the lens. For example, a aperture of f 2.8 is a large, wide aperture since the distance between the film and lens can be 'bridged' by only 2.8 apertures. A aperture of f 22 is a very tiny hole since it would take 22 apertures to stretch between the film and the lens. So the size of the aperture or opening gets larger as the f/stop decreases and smaller as it increases.
Every time you decrease your f/stop you are doubling the amount of light entering the camera, and every time you increase your f/stop you are halving the amount of light entering the camera. When you read the numbers on your lens this may not make sense since the numbers on your lens do not double (i.e. going from f 5.6 to f 4 doubles the light in the picture), but just trust me that it works. If you want to find out the entire story I recommend reading A Tedious Explanation of the f/stop.
Now the aperture affects more than just the light coming in the camera, it also effects the depth of field. The depth of field refers to how much of the picture will be in focus or out of focus. A high f/stop such as f 22 has a high depth of field, meaning that nearly everything in the picture will be in focus. A low f/stop of 2.8 has a low depth of field, meaning that only a narrow area of your picture will be in focus. For pictures were you want to show a lot of detail (such as landscapes) a high depth of field is preferable, while for pictures where you want to focus the viewers attention on something (such as a person in a portrait) a low depth of field helps by blurring out everything else in the picture.
This forms the basis of the next big trade off. A large aperture (small f/stop values) requires short exposure times but is difficult to focus while a small aperture (large f/stop values) requires long exposure times but is easy to focus.
The last element you have control over is the shutter speed. The shutter speed is the amount of time that the film is exposed to the light. This is measured in fractions of a second such as 1/250 s, 1/4 s, or even 8/1 s. Whenever you double the time the film is exposed to the light (moving from 1/500 s to 1/250 s or "stopping up") the picture will be twice as bright. When you halve the amount of time the film is exposed to the light (moving from 1/4 s to 1/8 s or "stopping down") the picture will be half as bright.
Shutter speed is important when you are taking a picture of something that is moving. For example, if you are taking a picture of a car passing right by you, a short shutter speed of 1/1000 s would show the car clearly, while a longer picture of 1/30 s would be blurred since the car traveled further across the picture while the shutter was open. If you were to take a picture of a moving car with a shutter speed of 16/1 s, in theory, the car would nearly disappear since it would be in the picture for only a fraction of the time.
One problem with film cameras is something called reciprocity failure. Film is really not meant to take pictures in low light conditions, so that nice doubling and halving that happens when you take pictures for double or halve the time breaks down when it is darker. Simply, reciprocity failure means your shutter speeds are going to be a lot longer than you think. Once you get to 1/1 s, in order to double the light in your image you need a shutter speed usually five time longer instead of twice as long. In some cases this makes taking pictures at night impractical, but if you are creative enough and willing to experiment with other settings and techniques, you can still manage to take pictures at night.
Now for the fun part, you get to see how this all works together. Since you are always doubling or halving the brightness of the image, the three elements of shutter speed, aperture, and film speed work together quite well.
For example, lets say you are taking a picture of a train using the settings of [1/80 s f 8 ISO 400] and you want to increase the aperture to f 16 to get a sharper (meaning: less blurry) background. This is a change of two stops (f 8 to f 11 to f 16). To keep the picture properly exposed you could decrease the shutter speed two stops to 1/20 s (1/80 s to 1/40 s to 1/20 s) but then the train would be blurry. So instead you would take the film out of your camera and replace it with ISO 1600 which is two stops faster (ISO 400 to ISO 800 to ISO 1600) and get your picture.
The practical implication of this is that [1/80 s f 8 ISO 400] is the same as [1/20 s f 16 ISO 400] is the same as [1/80 s f 16 ISO 1600] in terms of light. You can change any one of the three main settings of your camera, and balance the change with the other two based on what effect you want to achieve.
Star trails pictures are among the easiest night pictures to take if you are willing to invest the time. The idea behind these pictures is since the earth rotates once every day, if you leave the shutter open long enough you can see the stars move across the sky. Generally these pictures have a great amount of 'Wow!' factor and are a great way to get started with night photography in rural settings.
These are only things that I have discovered myself. They aren't always true and you can feel free to break them and play around a bit
What To Bring With You
The Short Version
In my opinion, the best way to learn night photography is to collect the recommended equipment and just hit the streets. I learned nearly everything I know about photography from trial and error, so I recommend it. Reading up a bit may help you, but it is no substitute for experience.