A good method is to honestly come to grips with your history. If you have been convicted of a felony and do not show or list that on your employment application your falsification can lead to termination if you are found out later. A background check is likely going to reveal your criminal past, anyway.
Describe the circumstances accurately. Be prepared to summarize how you have become a changed person. Outline how you are now armed with the ability to relate to at risk teens with a seasoned and experienced side of the story. Suggest this conviction in your past places you in a better position to help at risk teens avoid pitfalls and jump hurdles that they'll face.