This is the point that every first time brewer wants to get to and craves. The opportunity for first taste! There are a few things I need to mention about bottling.
1) A kit will likely come with a pre-measured amount of corn sugar. This is fine for simplicity sake, but corn sugar leaves trace off flavors that a good home brewer or a pro should be able to identify (not all can do this, but I hated hearing about it from pros when I first started). I have tried many different priming sugar techniques from honey to maple syrup, sugar, corn sugar, etc and malt extract for me gives the best results. Malt is after all what beer is made from, so naturally it should work best. I even find the smoothness of the bubbles made by malt fermentation to be superior to any carbonation method including force carbonation in a keg (draught beer). Therefore I recommend the purchase of Light Dry Malt Extract for bottling purposes. One and a quarter cups for a full five gallon batch (if your batch comes out less than 5 gallons, use less!).
2) Boil water with malt extract for 10 minutes, and pour it hot into the bottom of the bottling bucket. Transfer via siphon the finished beer on top of the sugar solution. This allows for equal distribution of the sugar for even carbonation thoughout the batch. When starting the siphon, the first little bit can end up in a little glass...
3) The bottling bucket can be a bucket with a valve added to the bottom, or a bucket without a hole. The former uses gravity feed, but requires an assistant to hold the bucket to get the beer below valve level out of the bucket through the hose and into bottles. The siphon method is easier for one person to do as the siphon sits on the bottom of the bucket. I prefer using a spring loaded bottling valve that fits on the end of the second half of the siphon.
4) My buddy and I saved bottles and accepted contributions instead of purchasing bottles. For those that plan on having more than one batch going at a time, lots of bottles are needed. Swing top bottles save time and the gaskets can easily be replaced when they go bad. Plenty of swing top beers out their at a good liquor stores! Go have a beer!
5) Depending on Original Gravity, the yeast used, and storage temperature, the beer may take anywhere from a few days to a couple of weeks or more to carbonate completely. If you are someone like me who enjoys a pint of cask ale at your local brewpub or tavern, there is nothing like cracking open a partially carbonated homebrew. It is the same thing: real ale!
Tip: I use a bottle tree to allow the water to drip off the bottles after rinsing off chlorine solution. It holds 45 bottles at a time and helps move along the bottle sanitization prossess a little faster as there is no need to wait for all of the water to drain off the bottle prior to moving to the next.