slipping transaxle

I am looking for information on finding out what is wrong with the transaxle on my sons car. I doesn't shift correctly at 3rd gear and slips in and out as you go down the road. If you make a turn either right or left it also goes out of gear. The manual I bought keeps telling me to take it to a professional. In the past I have had bad luck with them. I am looking for a way to get the info I need to fix this at home.