I started with a kit. For me, that was the best route to take. I had only a vague idea of the equipment needed for the process. My local store, DeFalco's, had all of the items I needed to get started. Since then, I have upgraded my equipment and added to it. It seems there's always room to improve. Most major cities will have some kind of homebrew shop that will have all the equipment needed. If you're in a more rural setting, you can always order kits and ingredients online.
THE MOST IMPORTANT PART IS THE SANITIZER!!!!!!!!
Any book you read, any forum you go to, all says to sanitize everything. Maybe I'm a bit OCD about it, maybe a little too sanitary with it, but I have not had a batch of beer go bad yet. *Knocks on wood.*
I purchased the kit and 2 cases (24 in each) of brown 12oz bottles. In retrospect, I could have been saving bottles for months leading up to this purchase. And I haven't purchased bottles since. Everyone's got friends and family that drink beer, have them save bottles for you. The only thing you have to watch out for is the types of bottles they give you. Brown (and blue) bottles are preferred as they let the least amount of light in, which can be damaging to the liquid inside. Green bottles are still acceptable. Things you do not want are twist top bottles and clear bottles.
With the kit, you are going to need some large volume kettle to cook everything in. Stainless steel is the preferred metal for these. An aluminum tamale steamer will not work as it will cause a metallic taste to get into the beer. Kettles can be purchased online or at the local homebrew store. It is also advisable to get one that is at least 5-gal (19L). You may want to get one that is slightly larger in size. I have found that a 5-gal kettle only really allows you to cook up to 4 gallons in the kettle at one time. Most books on the subject suggest getting one that is larger to be able to do the full boil, but we will go over that much later.
The last thing needed to begin is a set of ingredients. My kit came with the most basic recipe I've used to date. My suggestion would be to start with a recipe kit for your first brew. They will generally contain all of the ingredients needed for a 5-gallon batch of beer. This way you can get used to the process and how to use the equipment when needed.
Once these items are acquired, you're ready to get started brewing. For that first batch I did, I just followed the instructions that came with the recipe to the letter. It turned out well enough that I've continued to brew and try new things with it. Here's hoping the same happens for you.