You need to first start off with the effects first. You should know that all your effects in the processor should be turned off. The perfect jazz tone has no effects, except a reverb which you might want to add at the end. However, you should know that without any effects you can take out the perfect jazz sound and you will find it easy once you check it out for yourself.
The controls of your guitar should be set by you. Try to match them with any jazz guitar player of your liking. It is mostly considered as wise to try to use your guitar knobs perfectly. The EQ knobs should not be too high, while the tone should at least be at half. Try to listen to the sound of your guitar again and again so that you know what is perfect for you.
Once you are done with the first two steps, it is time to play your guitar. It will really help you understand the true sound of the guitar coming out. Keep playing different riffs so that you can understand the correct tone of the guitar that you are trying to play. Playing will really help you set the right jazz tone.
Try to put the gain down. This will help you totally neglect the distortion. Try to listen to the jazz guitar players; they rarely use distortion in their guitars. This really will help you keep going the way you want to. Gain is basically for rock, or grunge, but what you want to play is classy music and gain is not meant for you.
You should be careful about your amp and you should set its volume and its built-in distortion at the right level. You should know what sounds jazzy enough and then you will be able to make the right tone. Try to keep the treble high so that you it can detect each and every finger picking movement that you make.