Well I bought a kit and followed the instructions. It has bee 4 days now and I don't think I have seen my airlock move. I opened the top of my bucket and there was a lot of foam (bubbles). It also looked like brown skin so I stirred the brew and took a reading with my hydrometer and my reading is 1.020 now. Is my brew fermenting properly?
Agreed. Sounds like its going great, the reason the airlock wasn't bubbling is probably just the seal on your bucket is letting the CO2 vent out around the lid instead of through the airlock. As long as the layer of CO2 (heavier than air) sits undisturbed on top of the fermenting wort you should be fine.
I would think, a good way to tell, whether you have a good fermentation is the smell: If you put your nose carefully in the fermenter you should smell carbon dioxide. Of course CO2 does not have a smell as a pure gas, but the fermentation CO2 smells slightly (pleasently) sour. Be careful though to not put your head too far in, since the gas in the bucket has probably displaced the oxygen and the inhalation of CO2 will make you dizzy. ALso, you will risk contamination of the brew. It should not smell sweet or overly sour (i.e. like sour milk).