Arthur Hildersham: "The Doctrine of Fasting, and Prayer, and Humiliation for Sin Delivered" published in 1633. Never reprinted, but available from Early English Books Online if you have access to a decent research library.
Although not a Puritan in the strictest sense of the word (being Dutch), Brakel's chapter on fasting is rich, concise, and practical. It is the first chapter in Volume 4 of The Christian's Reasonable Service, available here.
Here is a very precise and concise puritan work on the art of fasting by the well known pastor-theologian Theophilus Ebenezer Wartnose. I include the full text for your perusal: