Once the bottles are all sanitized you must boil the priming sugar for 10-15 minutes. I use a cup of priming sugar and a cup of water. The yeast convert the priming sugar into carbon dioxide and the pressure inside the bottle that is created carbonates the beer. It's science.
In order to bottle, you need to siphon the beer from the fermenter to the bottling bucket. This is the point in which the priming sugar mixture is added to the beer. The force of the siphoning beer is sufficient enough to mix the two.
Two necessary tools for the job include a bottling attachment and a bottle capper (big red thing). The bottling attachment is a spring loaded tip that attaches to the bottling hose. It only dispenses beer when the tip is pressed to the bottom of the bottle. When the bottle is filled you pull out the tube and a perfect amount of head space is left in the bottle.
Once you fill a bottle it is best to immediately place a cap loosely on the top of the bottle and continue filling all of the bottles. Only after all the bottles are filled should you seal the bottles tight with the capper. The purpose of this step is to allow the yeast to create enough CO2 to push the oxygen out of the top of the bottle. Oxygen in beer can contribute off flavors, so this is one extra step to help improve the taste of your beer. When the bottles are filled seal them all with capper and you're done! (well sort of) It takes 2-4 weeks for the beer to condition. After 3 weeks you can finally drink. I have read that you should put the beer in the fridge for 2-3 days before drinking for best results, but let's be honest, after waiting 5 weeks, I pop one in the freezer and drink it 30 minutes later.