Start with a good introductory book...I recommend "Brewing the World's Great Beers" by Dave Miller. This book (and others) will have lists of gear needed. DON'T run to the homebrew store and buy a starter kit - probably has junk you don't want or need, and some of it you probably could buy cheaper at Target/WalMart. That being said, expect to spend about $100 on gear needed for a first batch. And if you like it, you'll spend $100s more over the years.
Gear needed from a speciality brewing store:
- fermentation bucket (or two, or a bucket and a carboy)
- airlock
- hydrometer to measure specific gravity
- racking cane + tubing (needed to transfer beer)
- sanitation stuff
- bottle capper, bottle caps
You might also want to seek out your local homebrewing club. They may have programs where you could buddy up with someone to brew a batch, and may open up opportunities to get recommendations on what to buy.