Cycling is what we need to do with our tank environment before we begin to seriously stock it with fish and inverts. Essential to knowing what is going on in the cycle, you will need a water test kit, that will test for ammonia, nitrite and nitrate [at the very least].
The "cycle" is actually short for the nitrogen cycle. The cycle begins the moment you introduce organic material, be it living, dead or a waste by-product, into your aquarium. In your case, your fish will excrete ammonia [the most toxic of the cycle chemicials] into the aquarium water. Natural "aerobic" [living in the prsence of oxygen] bacteria form and convert ammonia to nitrite, slightly less toxic than ammoinia. A 2nd group of bacteria form and then convert the nitrite to nitrate--the end stage by-prodcut of the cycle.
Ammonia is very toxic to fish and nitrite is less toxic but can still be deadly to fish. This is why fish die when a tank is new. They are exposed to ammonia and nitrite. When cycling or when adding any new organic material to your aquarium [fish, live rock, inverts] you need to have these kits at hand so that you can keep track of where your water quality is. To begin your cycle, your tank water will read high in ammonia. One day the ammonia will drop drammatically and the nitrites will rise significantly. When the nitrites fall, you will start to get nitrates. With regular tank maintence and water changes you will be able to keep the nitrates in check well enough to maintain a quality aquarium.
Now, the ugly brown stuff is an indication that your tank is cycling. This is diatoms or what hobbyst call “brown algae”. This is harmless and will cut back once your tank becomes established. In the meantime, you can clean as much of this up as you want by scrubbing it off the glass of your aquarium or lightly stirring your substrate.
Now, if you learned anything here, you should know by now that ammonia and nitrite kill animals. Thus, you do not want to keep adding more fish, or any organics to your tank while it is cycling. If you want to spare your existing fish, you can perform water changes when you see spikes of ammonia or nitrite. This will prolong the cycle but may save your fish.
Good luck and welcome to the board!