First of all I want to go over some of the basics of photography. I don't know how much you know about photography, so this may be a bit simplistic if you have some experience.
There are four basic things that affect the attributes of any particular photograph. They are shutter speed, aperture (also called f-stop or f-number), focal length, and ISO (the film equivalent of this is also called film speed). I am just going to through each one and talk about how they each individually affect how a photograph looks.
The first one that I am going to talk about is the simplest to understand, shutter speed. This is mostly because in some ways shutter speed has the smallest effect on a photograph. If you have a fast shutter speed you are more able to get a clear picture of something that is moving, while a slow shutter speed is more likely to be blurred because of either movement of the subject (what you are taking a picture of) or of your camera.
Next is aperture or f-stop. This can be somewhat confusing, so I am going to stay away from how much of an effect this has on the light that actually enters your camera and talk more about the generals of it. The aperture that you use is a description of how much light is allowed to enter your camera, or in other words, how big of a hole your camera is looking through. In very basic terms this is easy to understand, the bigger the hole your camera looks through, the brighter the image appears, and so the faster your shutter speed can be to get the same brightness of image. So, a bigger hole means that you can use a faster shutter speed, and a smaller hole means a slower shutter speed. Before I go on I should probably clarify something a bit. Apertures, or the size of the hole, are each given a specific number, and it is a bit opposite of how you think it should be. A bigger aperture has a smaller number. Weird yes, but there are some good, very confusing, reasons why this is, but I am not going to go into them. So, in very basic terms, an aperture with a number f2.8 is actually a bigger hole than an aperture of f4. (I hope you can see why it is called an f-stop or f-number now. )There is of course one more way that your aperture affects your picture, and that is is that it affects how much of the picture is in focus. A smaller f-number (bigger hole) has a smaller area that is in focus compared to a bigger f-number (smaller hole.) Here is where you start to see the trade off nature of photography.
Now on to focal length. This is quite a bit simpler than aperture, so you can relax a bit. Focal length is a description of the "zoom" of a lense. The bigger the focal length , the more zoomed in you are, and the smaller the focal length the more zoomed out you are. Another way to say this is that a big focal length is longer or telephoto, and that a small focal length is wider. That part is pretty simple, but your focal length also affects how your picture will look in a couple more ways. The first way is that a big focal length will make things look like they are closer together than a smaller focal length. An example is the best way to explain this I think. Lets say that you are trying to take a picture of your friend, with a mountain in the background. Let's say that you take a picture using a long focal length (more zoomed in), and then you take a picture using a small focal length, but you move closer to your friend so that they look the same size as they did in the picture where you zoomed in on them. If you compare the two pictures afterwards you would notice that in the picture where you were zoomed in the mountain in the background will look significantly bigger that it does in the picture that you took when you were zoomed out, even though your friend is the same size in each. Or in other words, in a zoomed in picture, everything looks like it is closer together than in a zoomed out picture. Focal length has one more effect though. It can also affect how much of your image is in focus. This part can be a bit confusing, so I am just going to go over the very basics. If you take a picture at a short focal length (zoomed out) you are usually going to have more in focus than if you zoom in. It is actually much more complicated than that, but that is enough for someone who is just getting starting on taking pictures.
And to finish it all off, ISO. This one is almost as simple as shutter speed, isn't that a relief! ISO on a digital camera is very much like film speed on a film camera. A higher ISO means that at the same aperture you can use a faster shutter speed. There are drawbacks to using a higher ISO though, and that is that higher ISO's are noisier than low ISO's. What this means in that if you take a picture with a low ISO and then switch to a higher ISO the higher ISO one will have more speckles, and not be as clear or sharp as the one that you took at lower ISO. Most modern consumer cameras can safely take pictures at ISO 400 without too much sacrifice in detail, but I wouldn't recommend going above 400. There are a few consumer cameras out there that can take really good picture at higher ISO's, but they are not very common.
Now that I've gone over some of the basic aspects of taking a photograph I'm going to go over some examples to help you get a feel for how this works in real life situations, and then I'll talk about aquarium photography in specific.
Lets say that you want to take a picture of your dog as it walks around the house or plays with a toy. You take a picture and it turns out blurry. You know that you have to use a faster shutter speed, so you take the easiest approach and up your ISO to 400. You try again and it turns out that the picture is still blurry. Now you have to make some harder decisions. Do you up the ISO into an "unsafe" region or change your aperture? If you increase your aperture (choose a smaller f-number) you could increase your shutter speed even more, but you will have to be more careful about your focus. In this case it would depend on if you think you can get the shot with a bigger aperture or not. If you think you can, then go for it! If you don't think you can, then increase your ISO, but realize that it probably won't look as good.
Now let's say that you want to take a picture of a really small snail. You get really close to it and take a picture, but when you look at it all that is in focus is a part of it's shell. Since the snail isn't moving very much, you can use a slower shutter speed in order to get a smaller aperture (bigger f-number).
A lot of photography is really about finding a balance between these four things in order to get pictures that look how you want. This is mostly the technical side of course, but it is helpful to those that wish they could take better pictures, as well as to the serious photographer. If you didn't understand anything or have any questions, feel free to post them.
And so now for some general information about taking pictures of an aquarium. You are usually going to want to not zoom in, use the biggest aperture (smallest f-number, biggest hole) that you can, and use a fairly high ISO (again, I would recommend staying below ISO 400.) If you are trying to get a picture of the tank mostly it is okay to use a longer shutter speed, but you will probably want to use a tripod and turn of your filter so that it doesn't blow any plants around. Fish are much trickier to get pictures of.