Do you already have the basic equipment to brew? Full boil or partial?
Definitely obtain a copy of Palmer's "How to Brew" and read Sections I and II to get a good basic understanding of the whole brewing process and to get you started.
Then do a
simple extract brew
with steeping grains, either from the samples in that book, a recipe found here, or from a purchased kit.
For example, I started out with a simple extract kit (steeping grains were included) from
http://www.homebrewery.com. My first brew was a Yellow Dog Pale Ale and that gave me a base of what was involved in home brewing and what a home brew tastes like. Without that first (basic) brew I would be flying in the dark for a long time. It turned out great, and tasted like beer!
The only thing about kit
instructions in general is that NOT all the DME (or LME) should be added at the beginning of the boil. Half at the beginning of the boil, and the rest 10 minutes before or at flame-out, which is the consensus on this board. I don't know if Palmer has revised or modernized any techniques in his 2nd edition.
Some kits have the (bittering) hops mixed in the extract, which doesn't give you the option to split the extract additions, but that is a minor issue, for the first beer. Some kits are better than others, so look around here to get some ideas.
After your first brew you will better understand the process and from there on learn more and slowly brew more complicated recipes with dry hopping etc.
Important Note:
One road to success is meticulous sanitation. Until it becomes second nature, each time you want to touch the wort (after the boil), or the yeast, STOP! Then review for yourself: "Did I sanitize?"