Ammonia = the waste that goldfish produce in their poop and from their gills is broken down into ammonia, this is toxic to the fish and can kill them in high (or even low) numbers.
NitrIte = the bacteria in the filter convert ammonia into nitrIte, this is also toxic to the fish and can easily kill them or leave lasting damage to their gills.
NitrAte = the bacteria in the filter take the nitrItes and convert them into nitrAtes, these are only harmful to your fish in high numbers. Weekly water changes are done to reduce the number of nitrAtes in the water. Plants can help too as they suck up the nitrAtes as food.
pH = the acidity or alkalinity of the water. Goldfish prefer a pH of 7 to 8, but as long as it is stable it doesnt really matter.
In an established tank ammonia should be at 0ppm (ppm = parts per million), nitrItes should also be at 0ppm, and nitrAtes should ideally be below 20ppm, if they get higher than 40ppm it could have negative affects on your fish like ill health and bottom sitting/lethargy, that is why water changes are important.
The dropper liquid test kits are good, like AP master kit.. here..
http://www.drsfostersmith.com/produc...188x003&ctt=60