Bring to a simmer over medium heat and cook for 5 minutes. Slightly mashing the fruit while it is cooking can release some of the flavor, but will also result in a slightly cloudier end product. If you want a nice clear syrup, don't mash the fruit.
Remove from heat and allow to steep for 1 hour.
Strain peaches through a fine mesh strainer.
Transfer the finished syrup to a bottle or jar with a sealable lid.
Notes
The peach syrup will last in the refrigerator for 2-3 weeks. For longer storage, you can freeze it. (Freezing it in ice cube trays creates single serving sizes perfect for adding to drinks.)