At this point, you're most likely sitting on 5 gallons of fermented goodness and it's hard to wait any longer to consume it. Truth be told, you certainly can drink the alcoholic beverage you've created in its current state (right from the fermentation vessel).
However, bottling your beer will allow you to keep it fresh longer, to add more carbonation, to chill it more easily, and of course to make it more transportable. Below are the recommended steps to bottling one's homebrew:
Gather or Buy Bottles
Lots of homebrew stores sell bottles, but you can also just keep and wash used bottles (it's more environmentally friendly too). As long as you make sure the bottle tops do not have twist-off threading any used beer bottle will do.
Wash them thoroughly (in a dishwasher is easiest with a very hot drying) and immerse in a no-rinse sanitizer just before filling.
Gather Bottling Supplies
Phone a Friend
Though the entire homebrewing process is much more enjoyable with a buddy, having a second set of hands, particularly for bottling, will make things go more smoothly. One person will fill, one person will cap.
Quickly capping after bottling will also ensure that the beer has minimal air contact, reducing the risk of oxidative off-flavors.
Add Priming Sugar to Your Beer
The idea here is to further carbonate your beer through creating a "second" fermentation in the bottle. Even if the beer has been transferred off of the primary yeast sediment there are still enough yeast cells in suspension to carbonate the beer.
The yeast just need more food, and that is the purpose of this additional amount of sugar (or another fermentable addition, such as honey or more malt extract). While it is best to consult your specific recipe, a good rule of thumb is 4/5 cup of white sugar or dextrose (corn sugar) per 5 gallons of beer.
If you want to be on the super safe side, boil this sugar first in a small amount of water to kill off any unwanted microorganisms.
Fill and Cap the Bottles
This process usually starts off in a very random, messy way, but once you have the rhythm down it is simply a matter of perseverance. Place the beer vesselup high enough so that either gravity alone (if using a bottling bucket) or the siphon works to release beer via the tubing.
A bottling wand has an internal shut-off valve that will allow the beer to flow only when placed in a bottle and is highly recommended. When capping, be sure that you apply a firm amount of pressure to the capper, but not so much that you risk breaking the bottle.
These primed bottles of beer will now need to sit undisturbed for about a week to allow the secondary fermentation to take place. Opening one too early is not disastrous, it will just be a bit flat and taste quite sweet for the style. The best storage area is a cool, dark place, similar to your primary fermentation conditions.