A basic test kit is something that anyone with an aquarium should have. The first thing you should do if you see your fish are acting different is test the water. You don't need a huge test kit that tests for everything, but a basic test kit with at least ammonia, nitrite, nitrate, and Ph is invaluable.
You should only see ammonia when your tank has not cycled yet. If you see any ammonia in an established tank there is a problem. There is either more ammonmia than your tank is used to dealing with, or the bacteria that make ammonia into nitrite have died. First think of reasons why the bacteria may have died. Have you cleaned your filter lately? Did you clean off the bio-balls or any other biological part of your filter? If so that might of killed the beneficial bacteria that convert ammonia into less harmful substances. The other thing is if there is a sudden increase in the ammount of ammonia and the bacteria can't keep up. This may be due to a dead fish that is rotting away, or a lot of over-feeding. Any level of ammonia that shows up on a test kit can be harmful to fish. If your tank is cycling the ammonia is normal, but if you see ammonia in an established tank, first remove the source of the extra ammonia if there is one, and then do large water changes until it is gone. An established aquarium should always read 0 ppm ammonia.
As with ammonia, you should only see nitrites in your aquarium during its cycle. Once the cycle is complete, an established aquarium should read 0 ppm nitrite. Ammonia is converted into nitrite, so if your established tank shows nitrites, you have to look for the extra ammonia source. If there is extra ammonia, it is converted into extra nitrites, so again look for anything decomposing in the aquarium. Like ammonia, if your established aquarium has a high level of nitrite you should do large water changes until it is gone. Nitrites are slightly less toxic to fish than ammonia, but if your established tank shows any trace of nitrites there is a problem, because under optimal circumstances there are bacteria that convert your nitrite to nitrate.
Nitrates are the final step in the nitrogen cycle. Your ammonia is turned into nitrites which are then turned into nitrates. This is good because nitrates are much less harmful to fish than either ammonia or nitrites, but nitrates can be harmful to fish in high concentrations. One of the primary reasons for water changes is to remove nitrates. In an established tank the nitrates will rise steadily until you do a water change. In a freshwater aquarium, you want your nitrates to stay below 50 ppm at all times, but the lower the better.
If you are new to aquariums your goal shouldn't be to have a high or low Ph, but to maintain a stable Ph. A lot of people reccomend testing your tap water and keeping fish that will be happy living in your tap water. The reason behind this is that it is difficult to keep your Ph stable if you try to change it. So if you test your tap water and it reads Ph 8.2, it would be good for you to keep african cichlids. If your tap water is Ph 7.2, you might want to keep tetras or the like. Even if you Ph is slightly higher or lower than your fish would like, I do not reccomend you use chemicals to try to change the Ph. The reason is that these chemicals can cause your Ph to be very unstable, and fish would rather live in a Ph slightly higher or lower than what they like, than a Ph that keeps going up and down. In fact, a large fast Ph swing can easily kill fish. So dont worry about keeping your Ph high or low, worry about keeping it stable.