As you revise, look at every word, sentence, paragraph, scene, even character with the question: is it necessary to the story? If no, take it out. If yes, ask yourself if there is a better way to do it.
Wordiness is one of the prime failings of inexperienced writers. Train yourself to be brutally honest with all your fine prose. If you have said something in two or three words, ask yourself if you can say it in one instead. If you have used two long sentences to describe something, can you say it in one shorter one? Or perhaps clarity would be better served if your long involved sentence were split into two shorter punchier ones. An overreliance on adjectives and adverbs is a major culprit in wordiness. Instead of modifying a verb with an adverb, search for a better action verb that tells it all. Instead of describing an object with two or three weak adjectives, search for one strong one. Learn to pack as much meaning into every word and phrase as possible and you will have come a long way toward producing clear concise writing.
Redundancy is another weakness to look for. Sometimes information needs to be repeated in order to reinforce it in the reader’s mind, especially when the plot is a complex one involving many characters. In such cases, it is usually enough to make a subtle reference to whatever it is you want the reader to remember, especially if it was presented in a thorough but entertaining way the first time around. Other than in such a circumstance, be careful not to bore the reader with a rehash of old news. Only return to it if you plan to build and expand on it for a specific purpose relating to your plot. Otherwise, out it goes!
Look at each scene with an eye to its usefulness. Does it advance the story and your characters' goals? What would result if it were eliminated? Or parts thrown out? Could it be combined with another scene in a way that would tighten the action? The same analysis should be applied to your characters. I once took a character out of a novel because I realized his function could be served by expanding the role of another character. It broke my heart because I quite liked him, but I steeled myself against my “grief” and acted for the overall benefit of the story.
It is difficult to take a hatchet to your own work. Every word, after all, has come from your heart and soul. That said, it is exponentially harder to face the judgment of a disengaged outsider. Yet that is the inevitable fate of any writer who hopes to sell his or her work. So do yourself a favor and be diligent on your own behalf. You will be glad you did.