One of the quickest ways to have a foul tank (foul in the sense of water quality), besides not changing the water frequently, is to not remove dead fish in a timely manner. This is a greater problem in smaller tanks. Also, heavily decorated tanks, especially those densely populated, can experience water problems when fish die and can't be seen. However, there are two reasonably easy ways to determine a potential problem before testing your water.
One is to perform a regular fish count. This involves counting your live fish. LFSs perform a count, but they count the dead, call a DFC (dead fish count). A good LFS will perform a DFC at least daily, if not twice a day or more. Regularly counting your fish will prevent fouling because a dead fish won't have time to fully decompose before you know it's missing.
A second method is to know the smell of your tank water. This will allow you to know that something is amiss, especially if you don't perform regular water tests or DFCs. If your nose is in tune with the smell of your tank water and you don't do a DFC, you'll know pretty quickly that something is wrong. The smell is distinguishable and unmistakable.
Again, a DFC may not be practical for densely populated tanks and won't work if you have a tank that houses fish of varying sizes in which larger ones are predators. Fish do eat fish, so one that is missing may have become lunch or dinner, which won't foul the tank. A DFC might not also be practical for larger tanks that are heavily decorated.
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