One thing I tell my students is to try reading your work out loud. Would you actually be able to "speak" your writing. Here are some more tips:
*check for the passive voice (the indirect format). The always sets you up to write wordy *eliminate wordy phrases such as "due to the fact that", and "I am writing you to tell you that" *avoid lawyer-like writing (herewith, the undersigned, heretofore etc).and other gobble-gook like phrases.
One problem that I run into is adjective and adverbs making my writing needlesly wordy. Now, I try to use them only when they effect the meaning of a sentence. Something else that makes writing too wordy is wandering off on subjects that do not contribute to the topic.
Use as few words to explain your meaning clearly. Use active verbs rather than passive ones. Read your work aloud. Edit out confusion. Never use many words where one would do, for example, "at this point in time" is simply "now" or "currently". "year on Year" is "each year" or "every year". Use plain English, rather than jargon. The Plain English Campaign's websites gives some good pointers on Plain English.