...Or perhaps I should say, read these. While brewing isn't necessarily complicated, there are a lot of things going on in the process and many ways to screw it up. You can learn the hard way, strictly through trial and error, or you can get a solid foundation with a little investment in time prior to brewing your first batch.
This is profound advise. Read about brewing! Books can actually teach you things.
Don't worry though, even after reading about brewing, there are still plenty of opportunities for trial and error. Here is the list of the three must read books on brewing beer, in the order of which to read them.
1. The Complete Joy of Homebrewing, by Charlie Papazian. This is the classic homebrewing book. While not perfect in every way, Papazian's style and enthusiasm for the hobby make this book perfect for the beginner. He even makes it seem easy. RDWHAHB. If you don't know what that means, you need to read this book. I suggest reading this before brewing your first batch.
2. How To Brew, by John Palmer. This book also covers the basics of homebrewing, and can work to both reinforce and build upon your knowledge of the craft. A great way to take it to the next level.
3. Designing Great Beers, by Ray Daniels. This book can get pretty heady. If the word spreadsheet scares you, or if looking at mathematical equations give you nightmares, then perhaps this isn't the book for you. If, on the other hand, you have a desire to really get to know how it all works, this is an excellent resource. You will learn things like determining the gravity based on the malts used, how to estimate final gravity, calculating IBUs, determining the amount of water needed, and a seemingly multitude of other goodies. The second half of the book focuses on different styles, their history, flavor profiles, and common ingredients used. Daniels presents a lot of data, and leaves you with the tools to create an excellent beer from scratch.
There are many other books and resources available. I venture to say that most brewers will have at least two of these books, if not all three in their library.