A petit theft charge is technically the State of Florida's criminal case against you. Thus, if someone's going to "drop" the case, it must be the State. However, sometimes an alleged victim of petit theft may come forward, and explain that--in fact--a defendant was not guilty of the crime as previously thought. Thus, if the 'second explaination' to the State sounds satisfactory, the State may proceed to drop their charges when convinced to do so by the alleged victim of the petit theft.
Of course, sometimes alleged victims of petit theft are so uncooperative that the State is forced to drop their charges. This can take quite a while, but I'll give you common example. A person is arrested for petit theft from a friend. The friend has the defendant arrested for petit theft, and then later feels bad about it, calls the State Attorney and requests that charges be dropped. The State doesn't drop charges just because a friend has had a change of heart, so the case continues forward. The friend, then, refuses to cooperate with the criminal proceedings, and the State--at the dawn of a jury trial--is forced to drop charges because their only witness to the theft fails to appear in court to testify against the defendant.
Anyway, the best way to have a petit theft dropped is to hire a local attorney to help you thru the process.
The crime is prosecuted by the State, not the victim. The State has an obligation to consider the victim's wishes, but they may elect to proceed with the case against you regardless of whether or not the victim wants them to. Hire a lawyer to help you defense yourself.
Those are very good answers. Although the State can go forward against the victim's wishes, they are unlikely to do so in the case of such a minor charge. It is too much of a pain for them to fight your attorney and their own victim.