Let's get to it...
Take a gallon of cold water, dissolve in to it 2½ lbs. of sugar, add a teaspoon or two of yeast, baker's yeast will do, mix it all up, pour it in to a clean fermentation vessel, and seal it with a bung fitted with a water-filled air lock.
The yeast will digest the dissolved sugar and release two by-products: alcohol and carbon dioxide gas. The fermentation vessel needs to be sealed from the outside air so that fruit flies, vinegar flies and harmful bacteria do not enter your brew and destroy it. However, the carbon dioxide gas produced during fermentation needs to be safely vented, otherwise the gas pressure within the vessel will eventually become so great that it will cause the vessel to explode like a bomb, possibly with lethal results. At the very least your equipment and your brew will be destroyed.
When the yeast has consumed all of the dissolved sugar the fermentation process is over. The resulting brew will have a cloudy, milky appearance, and there will be a sediment of dead yeast cells at the bottom of the fermentation vessel.
To remove the cloudiness, if it doesn't precipitate as more sediment, you need to add finings, such as isinglass, or a little brewed strong tea, or a little citric acid from oranges, lemons and the like. Such inclusions will cause suspended particles in the brew to precipitate down and form yet more sediment. When the brew is clear, siphon it off in to another vessel for subsequent bottling, with the siphon tube positioned above the sediment so that the sediment is left behind in the fermentation vessel.
Kilju brewing photo credit: © Photohound / Wikimedia Commons