Brewing beer at home involves four main steps: (1) making wort by boiling malt extract and water or soaking and draining grains, (2) primary fermentation where yeast is added to the cooled wort, (3) optional secondary fermentation or conditioning, and (4) bottling or kegging the fermented beer along with priming sugar to carbonate it. The process requires basic equipment like a large pot, fermentation vessels, airlock, and bottles or keg.