So after about 10 days - 2 weeks your beer should be ready to be bottled (depending on what you're brewing, could be even longer). First things first..
As mentioned in the Getting Started section, you're going to need plenty of bottles, enough to facilitate 40 pints if you're brewing a 5 gallon/20 litre batch. The bottles will need to be thoroughly cleaned and sanitized of course, you don't want to have come all this way to spoil your beer now! Clean your bottles using a bottling brush and a bleach solution - take extra care if you're using used bottles that need a good scrub and careful not to break them in the sink! give them a decent rinse after wards and leave them somewhere to dry (a bottle drainer is a handy tool to invest in) The cleaning process can be done in advance of your bottling day as you'll will be sanitizing closer to the time. If you're going to re-use bottles, get into the habit of giving them a quick rinse under the tap with some warm water, make sure there's nothing left inside and leave them somewhere handy for another day. You can also buy bottles from a bottle supplier or home brewing goods store. Swing top bottles are great for their versatility but I usually use plain glass beer bottles with crown caps and a bottle capper - the caps are cheap to buy and if you break a plain bottle its not as much of a loss that breaking a swing top bottle.
So when you're about to bottle your batch, get your collection of clean bottles ready. Using a 'no rinse' sanitizing solution in a basin or sink, immerse a few bottles into the sanitizing solution & allow them to fill up completely. give them about 30 seconds or so and then drain and leave on a bottle rack or somewhere they can stand upside down to dry. If you have a dishwasher with a heat dry setting, this can be used to sterilise clean bottles too. once you have sterilized and dried your bottles, keep them somewhere handy and maybe throw a paper towel or clean tea towel over the top to stop any thing getting in (it's unlikely they'll get contaminated but you don't want to have to go through the whole process again because someone sneezed all over your bottles by accident!) If using crown caps, put them into a bowl of sanitizing solution
Preparing for Beer to go in the Bottle/Priming your Beer
You'll need to prepare a small amount of sugar for each bottle - the yeast in the beer will eat this and release CO2 into the sealed bottle thus carbonating your beer. Normal sugar can be used as we'll only use a small amount. You can add about half tea-spoon of table sugar for each 330 ml (12oz) bottle or just a little bit more for a 500ml (16oz) and fill the bottle up on top of this. You can also get 'carbonation drops' which are basically lumps of sugar you can add to the bottles that will dissolve, also more convenient.
If you are using a bottling bucket however, I strongly recommend a method called batch priming. Batch priming is basically making up a solution of sugar and water and adding it to your bottling bucket before you transfer the beer. Also with batch priming there are alternatives to sugar that can be used with positive effects (EG - Wheat malt extract is said to contribute to a good head retention), depending on the beer style you've brewed you can look into different alternatives. When making your priming solution be sure to use the right amount of sugar to get your desired level of carbonation. There's a few calculators online that will help you with this, one I use can be found here - it also gives an indication onto what beers should have more/less carbonation. The rule of thumb I use is the darker the beer, the smoother (less carbonated) you want it to be (stout for example), but there are some exceptions to that rule. Then to actually make the priming solution, add 1 part sugar (or whatever you're using) to 2 parts boiling water (eg 100g sugar/200ml water), boil it all in a pot for 5 mins to sterilize it (watch out for boil overs), cover and let the solution cool to about 30°c or less. once cooled add it to your bottling bucket and rack your beer from the fermenter to the bottling bucket, using a syphon, on top of the priming solution. The benefit to this method is that while your beer is being racked to the bottling bucket, it will evenly mix around with the priming solution so you wont have to worry about one bottle being more carbonated that the other.
Getting the Beer into the Bottle
There's a number of ways for you to start doing this but the best way is to use a bottling bucket with fitted tap/spigot & bottling wand. A bottling wand (aka bottle filling stick) is basically a plastic tube with a valve on one end, when you press the valve end against the inside base of the bottle beer comes out with minimal splashing. This can also be used with a syphon too if you don't have a tap fitted. You can also buy taps with a bottling wand fitted (IE 'Little Bottler') but if you don't have one for your tap, try get your hands on about a foot of food grade tubing/hose that you can fit to the end on the tap to make a filling tube - you'll have to turn the tap on/off while filling but it'll reduce and splashing around of your beer. Regardless if you use a tap or syphon, gravity will be your friend here so try get your bottling bucket up at a decent height. I put a wooden kitchen chair on the kitchen table, making sure it's sturdy, and put the bottling bucket full of beer on the chair with all the empty bottles below the chair ready to go. Other people might just use a table/counter and bottle from the floor but after a few bottles have been filled that position might get a bit uncomfortable.
When everything is ready, get your first bottle and place the bottling wand/filling tube right down the bottom and start filling, fill the bottle right to the lip at the top - once you remove the bottling wand/filling tube from the bottle it will leave about an inch or so of space. Get a crown cap ready, shake of any sanitizing solution from the cap and place it on the top of the bottle for now - don't seal it with the bottle capper yet. If using swing-top bottles just let the lid sit, don't lock it on yet. Place the bottle to one side and repeat the process until you run out of beer. The reason for not using the bottle capper yet is that in the few minutes it will take for you to fill all the bottles the yeast will release some co2 out, pushing out/ reducing oxygen from the space at the top of the bottle. Remember Oxygen = Bad for fermented beer so the less oxygen in your bottle, the longer it will last. When all your bottles are full, go back to the first bottle you filled, and use the crown bottle capper to seal the bottle or if using swing top bottles clamp the lid down. -Congratulations!! You've just bottled your first home-made beer!! Seal the caps on the rest of your bottles and store them, in the same area you had your fermenter in, at room temperature for about 10 days to 3 weeks (again depending on what you've brewed) to carbonate & condition in the bottles.