William Strunk wrote (E.B White edited and added to) a small book called The Elements of Style. It's filled with practical points for becoming a better writer, and it's a necessity for every writer's tool belt. It's not wishy washy, indefinite, or outdated, even though it's nearing 100 years old.
Much of it is instantly applicable, but (in my opinion) nothing more than the directive regarding word usage.
Writing is any man's game, but not every man's masterpiece. Needless words separate the mediocre from the good, and the good from the great.
A few ways to omit needless words (and become one of those great writers):
#) Edit. Seldom is anything slim enough in the first draft. Or the fourth. Or the seventh. Put it aside for a few days, then come back to it. Several times. You'll be surprised at all the unnecessary words you use.
#) Give yourself a word count. In college I took an editing class. We had a guest lecture from a teacher who gave us the assignment to condense a famous 350 word story into 100 words or less, but preserve the intended meaning. It was difficult, but not impossible. Having a limit is a good way to learn discernment. If you're thinking does this phrase really matter, it's likely that it doesn't.
#) Say it a few different ways. Good writers will come up with several ways to say something before they settle on their favorite, or combine a few of them. This ensures the best content and the best style.
#) Be hard on yourself. All through high school I had a running joke that letting people edit my writing was like watching them kill my children. Morbid, I know. But every writer knows the feeling—watching words get cut is like waiting in line for cake for four hours, and watching the person in front of you walk away with the last piece. It's miserable, hopeless, and depressing. But when your final draft is slick and clean, it's worth it.
#) Practice. It wouldn't be one of my how-to lists if I didn't tell you to practice. Ballerinas don't get good sitting on the couch. Chefs won't improve if they only make instant pudding and grilled cheese. Children don't learn how to walk without falling over. A lot of times.
Get rid of those words. Nobody wants them anyway.
Purchase The Elements of Style. If you don't own a copy, you need one. Non-negotiable.