Alright, where to begin? A great many beginners in fish keeping do not know about New Tank Syndrome. For example, you set up a new tank, and in a couple of hours you buy fish; 24 hours later your fish are dead. What happened?
Well, three main things happened:
1) You bought fish too early
2) You didn't cycle your tank
3) You didn't test the water perimetersCycling a tank, regardless what type of filter you have, is a vital part in having fish. Compounds like lethal Ammonia (NH3) and dangerous Nitrite (NO2) build up too quickly and have to be converted to less damaging compounds. You have two options in cycling a tank: fishless cycling, and fish in cycling.
Fishless cycling: This doesn't involve fish, so this is the best option. Since bacteria break down Ammonia into Nitrite, and Nitrite into Nitrate; we love these guys. Or at least I do! Now, the easiest way to start a fishless cycle is to put a lot of fish food in some sort of mesh; for example, tea bags work great- if you dump out the contents and rinse in hot water first. All you do is hang the bag in the aquarium, and let the food rot. I'd check the water perimeters either once or twice every couple of days (or once or twice every week or so if your low on test equipment). Once a steady climb of Nitrate (NO3) starts, do a 25-50% water change and your ready to go!
Fish in cycle: I don't recommend this type as it is very stressful/harmful to the fish. Basically you put ONE very hardy fish in the tank and feed it and such, but you have to test/change the water every day or two. Yea... I don't recommend this.