I'm embarrassed to say that when I decided to become a writer, it was about 18 months before I got around to picking up this seminal work on the craft. To my folly, I had churned out two drafts of my first book, and hundreds of other pages of content for other works before even acquainting myself with the basic wisdom enshrined in this book.
This is a thin book, and deliberately so; one of its main points is that good writing should be concise. "Let every word tell." It's got lots of great advice, but maybe it's a bit too thin, so I suggest you also check out the Cassell's Guide To Written English too.
If you want to be taken seriously in the written word, Strunk & White is essential reading, if only so you can drop the name around other writers and boost your street cred.