Read your kit instructions for adding yeast. More than likely it will be a dry yeast that needs to be rehydrated in warm water before pitching. Make sure that you take a hydrometer reading to determine your Original Gravity (OG). This is important to help you determine later in the process when the fermentation has completed. Make sure you seal the fermenter and insert the airlock or blow off tube.
At this point you sit back and wait, and let the yeast go to work turning your wort into beer. Your package of yeast should tell you what the ideal temperature range is for fermentation. It is critical that you keep the beer within this range at a steady, constant temperature.
The fermentation process takes about 10 days to complete, but the only definite way to know it is done is to check with your hydrometer. If you take readings on consecutive days and get the same reading, and that number is within 5 points of your target Final Gravity, then fermentation is complete. The instructions in your kit should give you your target FG.
You can then decide if you want to transfer your beer to a secondary fermenter, or just leave it in the primary for a couple more weeks. Fermentation does not actually happen in secondary fermentation. You only rack to a secondary once the process of fermentation has completed.
The secondary fermentation is done to clarify and condition your beer. Not all brewers secondary ferment, and for many types of beers, it isn't necessary. You can research online into this a little further to see why you would and would not want to secondary ferment. From there, you can decide what way works best for you. It doesn't hurt the beer to leave it in the primary for a few more weeks as opposed to racking to the secondary after fermentation is complete. In fact, it will actually make your beer better.
Many kit instructions will tell you that your beer only needs to ferment for a week, and then soon after it will be ready to drink. Ignore these instructions. Leaving your beer in the fermenter for 3-4 weeks, whether you secondary ferment or just leave it in the primary, will make much better beer. It may be tough to wait that long, but it will be worth it.
Once you have completed fermentation, you are now ready to bottle.
First, make sure that the bottles have been sanitized, as well as all theCommercial Beer Brewing Equipment you will use for the bottling process--siphon, tubing, bottling wand, caps, and bottling bucket. Your kit may tell you to add sugar to each bottle, but a better way to do it is to take the total amount of sugar called for and thoroughly dissolve it in some boiling water. Let that mixture cool to 70F degrees, and then add that to your bottling bucket. Then, rack your beer into the bottling bucket and take care not to let the beer splash. You can use a siphon to transfer the beer. Here is where it helps to have an auto siphon. If you do not have one, do not use your mouth to start a siphon because your mouth has bacteria and germs that can get into your beer.