Questions about starting your own homebrewery always start after taking a sip of homebrew and realizing that it is not just something the brewer made up in their guest bathtub. There are negative connotations about making alcohol in a residence but it just takes that one spark to want to do it yourself. There are many different ways that one could go about starting their own homebrew operations. I'd like to post somewhat of a guide if you are thinking about getting into this great hobby.
As a disclaimer I would like to explain that if you choose to get into brewing your own beer it will not be done cheaply. Sure, if you look at the cost of ingredients and how much return you have with the final product it seems that you are not spending as much as you would at a liquor store. However, as most h-brewers will tell you, from that first time your own beer hits your lips you want to improve your processes and your equipment which gets to be somewhat expensive. The great thing is that you can still keep brewing while adding a piece here or a piece there.
A great first step would be to first join someone else on a brew day. This will get you accustomed to the process and the work it entails. I have known many award winning homebrewers who have started this way. Generally most homebrewers are glad to share knowledge, their systems, and their all around joy for the hobby.
If this is not an option for you its no big deal. I got into the hobby all by my lonesome. I started by receiving a Mr. Beer kit from my girlfriend for Christmas.
You will hear mixed reviews about the above mentioned kit. My reason for recommending it is that it is simple, lays out step by step instructions, cheap (can be found at after xmas sales for like 15 bucks), smaller scale, and can be done on an electric stove top. The few others pieces of equipment you'll need, which are usually available around the kitchen, are a 12 quart stock pot and a stir spoon.
The extract and hops are sometimes stale and you might not turn out the greatest beer but what this kit does is gives you an understanding of the processes that take place to create beer. This doesn't really matter though because the first beer you drink that you have created you will think is the best beer in the world.
After making a few batches with the included Mr. Beer ingredient kits my interest started to spark and I researched the internet. I found out that people out there are actually really into this and that there was a store that sold fresh beer making ingredients a town over from me. This left me wanting more out of my creation and I began using the same equipment from the kit but buying fresh malt extracts and hops from the homebrew store. Gradually over time my batch size grew and my equipment got better, thus resulting in a better homebrewed product. I owe it all to my girlfriend and that little kit she got me for the great hobby and the few medals I have hanging on my wall.
An absolute must is to purchase the book How to Brew by John Palmer. This is commonly referred to as the "homebrewers bible" an electronic version is also available here.
Another great starter book is The Complete Joy of Hombrewing by Charlie Papazian.
Both of these books will give you all of the information you need to start brewing your own beer. They both range from aspects for the beginning brewer to the most advanced practices of the all-grain brewer. They are invaluable to have and will be your companion throughout the homebrewing journey.
Another way to start is to look around the internet or find your local homebrew shop and take a look at their starter kits. Most hombrew equipment providers will have made up kits that have all the basic necessities. When looking at these kits I would recommend that you talk to someone at the store and ask about other pieces you may need. These kits usually don't include other necessities like a pot big enough to boil your wort, the bottles needed storage, etc. Some of the larger pieces are quite expensive so take a look around at your local thrift store, you'll often be able to find things at a fraction of the cost. Here is a link to one of these starter kits, I have ordered quite a bit from this online store and find them a quite reputable source of supplies.
Ok, so you have obtained all your equipment and are ready for your first brew. Now the issue is developing a recipe. Generally speaking there are two different types of brewers, all-grain and extract. All-grain is the more advanced method which includes a mashing step where all of the sugary wort is extracted straight from malted grain. As a beginner it is highly advisable to start in the extract realm. Extract comes in two forms, liquid and dry. You can obtain these from any home brew store.
To simplify even more, homebrew stores will often have ingredient kits that include everything you will need for your first brew. This is a great idea for your first few go rounds so that you will get used to the process, these kits are tried and true recipes that have been perfected. You can get an idea of these kits here. They will provide step by step instructions that will help you through the steps. Soon after you get the process down you can branch out and begin partial mashes. This is in between extract and all-grain brewing, malted grain is incorporated in the brewing process by steeping in your brewpot. Partial mashes gives a beginning brewer more options while still keeping it a simple/short brew day.
It's hard to explain where to start but I believe most of what I have said will apply to mostly everyone. People have different set ups in their house and different items that have been collected along the way that can be applied to homebrewing. After reading the beginner sections in the books listed or discovering the brewing process in another way you'll have a better understanding of what you specifically need. And remember, always follow Charlie Papazian's code "Relax, don't worry, have a homebrew."