Often times what makes a strong image are the very elements that we tend not to pay attention to, the background. Being able to control the non essential (but still critical) portions of the photograph will often take your photograph to the next level. Whether taking pictures of your Discus, other family members (!) or birds in flight, keeping non distracting elements out of the background is something you should try and think about as you plan and compose your shot. Sometimes the surroundings are an important part of an environmental image and you might choose to have that in focus, but most of the time the viewer's eye should go to the subject and not be distracted by stuff in the background.
So as you take more shots, think about what is behind the image and how you can control the setting. For your Discus darken the back of the tank (if you don't have a solid BG already). Take some test shots of that area and see if there are any distracting elements. Instead of chasing the fish with your camera, be patient and wait for the fish to pose in that part of the tank (a tripod helps!) and fire away. The greater the distance from the subject to what's behind it the more the BG will be rendered out of focus. So if you have a wide (front to back) tank the better the background will appear. You can also dictate the background from the camera. People want the best detail in their fish so they set a high f stop, 16, 22 and now more of what is behind the fish will be in focus and potentially distracting. If your flat fish is parallel to the lens you will get a sharp subject with f 8, 5.6 or even f4 and the BG will be a pleasant blur. You are controlling the depth of field. (Even if the fish is straight on looking at you, the face and eye will be in focus. Lighting, black backgrounds etc. are a subject for another time.)
If you are reading a lens review at some point you will see the term Bokeh. Your eyes glaze over and you ignore the rest of the article. Bokeh is a Japanese term (BOH-kay or BOH-ka) and is defined as the way a lens renders out of focus elements, points of light. This is pretty important when considering how your image background will look. Most lenses today have pretty acceptable Bokeh, some do not, and some have beautiful Bokeh that really makes an image special. Where it is important is in macro (often used in fish photography) and telephoto lenses. The physics is not important, but understanding that there can be a difference in the quality of Bokeh is of note, especially when it comes to putting down money on a lens.
Some BG distractions can be removed with the computer in post processing. But, it is best to clean up the image in camera and leave little work to the digital darkroom.
I went out yesterday and shot this series of images of a Milkweed pod:
The first one has a little too much depth of field and the white blob (center) and bright yellow leaves (bottom left) are way too distracting.
Attachment 91368
So I moved to the left a bit. The bushes in the BG were a bit further away and I went from f11 to f8. There are now two new white blobs. The middle one might be hard to get out with the computer.
Attachment 91369
So I moved the two white flowers in the BG out of the way. Now I like the BG. I also got lucky with a little selective ray of sun.
Attachment 91370
I have spent a lot of time photographing a Common Tern nesting site. At first I was just glad to get a bird in focus. The I started to think about a bird in focus with a nice BG. Watching how they were landing to feed the chicks, I placed my tripod low on the sand to shoot upward to get a blue sky BG but I also wanted a green line of out of focus grass. I took several shots just to be sure the BG was OK. Then I had to wait for a Tern, with a fish, to "fly into my picture". It took several hours. The soft grass is a function of the f stop but also of the lens which has beautiful Bokeh!.
Attachment 91371
So think about what's behind your subject as you point the camera. Get critical of the background. I think it will make for better images.
