The best preparation for a Zoning Board of Appeals appearance is to attend a hearing before your own hearing is scheduled. By listening to the presentations and the questions asked by the Board, you will get a sense of the workings of the Board.
A Zoning Board of Appeals Hearing, while quasi-judicial in nature, is still relatively informal. The Board goes out of its way not to be intimidating. After all, the members of the Board are all volunteers, and are your neighbors.