There are several reasons why you would want to make your own beer: as a hobby, as a way of trying different flavors that you can't find with the big brands, or even as a way to save money by trying to reproduce some expensive craft beers.
Whatever your reason, brewing beer on your own is not as easy as baking a cake and there's a lot more equipment involved. You will need at least: a stainless steel brew pot, a fermenter, a spiral immersion chiller, thermometer, hydrometer, airlock, bottles, caps, bottler capper, bottle filler, tubing, sanitation solution. Not to mention the ingredients: malt, hops, yeast and optional flavoring ingredients.
If you try to buy it all separately for the first time, you may easily get overwhelmed by the variety of both equipments and models available. And your chances of success with your first batches are greatly diminished.
The best way for aspiring home brewers to get started is by using a Home Brewing Kit, also known as Starter Kit. These kits come with all the gear you'll need to make your first batch of beer plus the ingredients, usually in the form of malt extract, yeast and fresh hops.
Basic home brew kits come with a plastic fermenter and a plastic bottling bucket with a spigot (both usually 6 gallons), thermometer, hydrometer, large stirring spoon, airlock, siphon, sanitizer solution, bottles, caps, bottle capper, ingredients (beer kit with malt extract, brewing sugar, brewing yeast and carbonation drops) and a step-by-step instruction DVD or book.The brew pot usually is sold separately.
There are different home brewing kits, ranging in price from under $100 to over $400. The difference here is both in the size of the buckets - which allows for more or less beer in each batch - and in the quality of the equipment. Some kits will include kegs, for those who don't want to bother with bottles, although bottling will help in beer maturing and is preferred by those who brew ales. If you are brewing lagers for the hot summer days, then kegging might be an option. Remember, though, that lager is considered more difficult to brew than ale, especially because it requires colder fermenting temperatures. So if you are an absolute beginner, you might want to go with ales.
The great thing about these kits is they can be used over and over again - you only have to refill the ingredients as they are consumed. As you gain experience, you may want to replace some of the equipment in your starter kit with more advanced items, or bigger ones if you want to increase production. By this time, you will have a much better knowledge of what and where to buy.
Eventually, you will replace the starter kit your own custom one, with all your favorite home brewing supplies, the perfect setup to suit your brewing needs and preferences.