Slice the peaches, you should be able to get 6 - 8 slices out of each peach. Slice the goat cheese, I find this to be the easiest by placing it in the freezer for 10-15 minutes and using waxed dental floss for the slicing rather than a knife.
Divide the arugula between 4 salad plates. Then layer the salad in a stack alternating peaches, basil, goat cheese. I aim for 3 layers of peaches and basil and one two layers of the cheese.. If you have large basil leaves most likely just one per layer will be needed, if they are small ones from your yard then 2-3 per layer. Drizzle each salad with oil and vinegar.