There are many ways to flavor moonshine, but the easiest way to do it is to add the fruit directly to a jar of finished shine (or vice versa). Cut the peach into slices or (if they're small enough) stick two or three whole peaches in a quart jar, add shine, and leave it sit.
Here's the thing: you can infuse just about any ingredient into whiskey. Fruits, vegetables, herbs and spices are the most common ingredients to infuse with whiskey. Believe it or not, you can also work with butter and cheese or fat-wash whiskey with smoked ham, cooked bacon, charcuterie and other meats.