Pick up a copy of, "Merriam-Webster's A Dictionary of Prefixes, Suffixes, and Combining Forms." Use this to learn how words are put together. This book can be found online or at a local bookstore.
Check out the official National Spelling Bee guide called, "Spell It!" Find it in your local bookstore or online.
Study the Consolidated Word List link that is listed below. It is a compilation of spelling words dated back to 1950. The words are categorized between words based upon frequency of use in spelling bee competitions.
Check the local newspaper that sponsors the spelling bee for a list of words to be used during competition time. Sometimes they are given the list as a guide to help students study.
Look for more word list resources at libraries or bookstores that carry study material for standardized tests (i.e. ACT or SAT) They have verbal sections dedicated to vocabulary words.
Pick between 50 and 100 words that should be studied on a weekly basis. Write down the difficult words many times and learn how to incorporate some of those words in normal conversation.
Practice spelling the words out loud and then time yourself. In competitions, a person is given about 2 1/2 minutes to spell the word.
Ask a friend to help test you on what you've learned.