Well Francis I am still a little new to the hobby but I will give you the basics for starting.
First and most importantly:
"The Joy of Home Brewing" by Charlie Papazian
Go buy it, read it, study it, sleep with it under your pillow, etc.....
You get the point. It is the bible of brewing. This book will discuss all of the equipment, ingredients, and procedures you need to know.
Here is an online book about brewing:
http://www.howtobrew.com/intro.html
Second:
Find a local HBS (Homebrew store) and order your equipment. You should be able to put together a list of equipment from Papazian’s book. If you have a local HBS then someone there should be more then willing to help you pick out equipment. It sort of sucks if you don't have a local HBS, but you can get away with ordering everything from the internet. You just get stuck with paying shipping charges and these shipping costs can be a lot for your initial equipment purchase.
Here is a link for the store I use. This store is local to me, but they also do internet sales. Shop around for online stores if you don’t have a local one!
http://www.ebrew.com/
Third:
Locate and join a brewing forum. Folks on beer/brew forums are very friendly and are always willing to answer questions you may have. Two that I can recommend (but there are others out there):
http://forums.homebrew.com/
http://forum.northernbrewer.com/
Forth:
BREW!!! Now that you have read the book, bought the equipment, and had all of your questions answered, it’s time to brew. Sanitation is about one of the most important steps in the process. If it is not sanitized, then it must never touch the brew!!! You’ll read all about it in the book. When you first start brewing it will be with extracts instead of all grain. You can read about the differences between the two. Extract brewing is very easy for the beginner and takes a less time and equipment then all grain brewing. You usually can buy an extract kit that has everything you need including: Malt extracts, specialty malts, bittering hops, flavoring hops, aromatic hops, fining additives, sugar for bottling, yeast, and instructions. I am currently extract brewing while I collect and build the equipment for all grain brewing.
The downside: You will be waiting for 4+ weeks before drinking your brew. The longer the better!!!
Due to lack of time I am going to cut this short. Charlie Papazian's book is going to give you all the information you need. It may suck waiting to read the book before brewing, but DO it. You will have less mistakes and you will not be questioning things on brew day. If you or anyone has questions along the way please feel free to ask me. Try to keep it to this thread.