How do you repair the transmission of a riding lawn mower?
Generally speaking, if you have to ask, then you should let a professional mechanic do the repairs for you. Regardless, you did not specify the make and model of the riding lawn mower, nor did you even indicate what is wrong with it, as it may have nothing to do with the transmission, and, even then, nobody can diagnose problems or suggest solutions without seeing the vehicle, so it is virtually impossible to your question.