The most common way that people train for a spelling bee is by making word lists. The speller will copy words out of the dictionary onto index cards or a notebook--it's important to copy them by hand as that helps the speller remember them, and then she will read and reread the word until she feels confident that she can spell it under pressure. It's important that the word lists not be copied in strict alphabetical order as they will not come up that way in the actual spelling bee.
During the actual bee, the participant has to spell out words given to him by a person called the pronouncer. Simulate this situation by employing a spelling buddy who reads words aloud for you to spell. This helps the participant prepare for the actual circumstances of the spelling bee, and is excellent spelling practice. One very important part of the training process is to hear words spoken rather than just reading them, because the pronouncer on the day of the bee may say something slightly differently than expected. Using a spelling buddy helps the participant prepare for this.
Sometimes, in addition to making word lists and using a spelling buddy (who may be a friend, sibling or parent), a spelling bee participant hires a spelling tutor. A tutor is a person who frequently works with spelling bee participants and therefore knows what types of words are likely to be asked, what happens on the day of the actual bee and proven methods for success. Spelling tutors are used most frequently at the highest level of spelling bee competition, and often have a repertoire of techniques honed over years of helping spelling bee participants.
Another fun way to stimulate the brain is by playing interactive word games. There are many free games online that simulate the actual spelling bee by asking the participant to listen to a word and then spell it out; the only difference is that the participant is typing rather than talking. Certainly no online word game is going to be detrimental to a would-be spelling champion, but it's important to focus on the games that mimic the actual bee--as many online word games use shorter words that would never come up in competition. Interactive games may also seem more fun than making out word lists, but it's important to employ a variety of training techniques before the big bee.