The Florida courts have a website (see below) that tells you what the process is.
You need to have all your receipts, all the warranty information and proof of what you paid.
In addition, you should check with the company that issued the warranty (the car manufacturer?) and find out
1) if the work would actually be warranty work and
2) if it would, would they reimburse you or
3) would they reimburse the mechanic's shop so that you would get a refund?
Be prepared to write your testimony - keep it short and to the point, but include all relevant facts. While you can express an opinion, your testimony should let the facts speak for themselves. Have someone else read it to see if they get out of it everything you want the judge to. Check the spelling, number the pages. Submit it according to the court's rules.
Once in court:
Be prepared to show all your evidence.
Be prepared to answer questions and to provide your side, particularly in those areas where your testimony and theirs aren't the same.
Dress properly (shirt and tie if you're a guy, a demure dress or sweater if you're a gal)
Call the judge "your honor" and speak politely
Take someone with you to take notes and ask as moral support.
Good luck!