Hebgen Lake is a special place during the warmer summer months. It is formed by the Madison River just outside the western boundry of YNP and just a few miles north of West Yellowstone, Mt. (West Entrance to YNP). There is very good access by a multitude of roads to almost all of the lake.
I have found that the "Madison Arm" or the eastern most part of the lake is the most productive area for the fly fisherman. It tends to be more shallow and has more weed beds that support the aquatic insect populations (calaebaetis and tricos mostly).
It is commonly called "gulper" fishing by many that have experienced it. They are called gulpers because you can often hear them "gulping" as they take flies off the surface during the quiet of early morning. It is best fished from a boat but my strong preference is a float tube or small plantoon boat because you can get closer to the cruising pods of trout. A #16 adams is the most popular fly but when they are really going, they will eat almost anything so long as it is not too big.
This is a morning thing as the wind will often come up in the late morning/early afternoon and the trout are very hard to spot. Do not let this fact keep you away...the Madison River either in the park or the great stretches below Quake Lake are just a short drive away. I am sometimes reminded of fishing for bonefish on the flats as these fish cruise around and you sight fish to them leading them much like you would a bonefish.
I have spent well over 100 mornings on Hebgen over many years. When I first discovered this treasure in the mid 1970s, gulper fishing was almost a secret but it has since become very well known. Unless the wind comes up super early, you are almost guaranteed to catch fish. They average 16-18" and browns and rainbows are about equal in number. Typically, a 25-30' cast is sufficient. I have had 20 fish mornings on numerous occasions.
I strongly suggest 12'+ leaders and 5X tippet. You will be most successful if you can make a quick cast (1-2 false casts maximum) to 25' or so. Accuracy, although important, is not as critical as it would be in many stream situations. You can increase your number by dropping a small nymph 12-14" below your dry fly.
(video ): Montana Gulpers (Big Trout) - by The New Fly Fisher
Hebgen Lake - by montanatroutonthefly.com
Hebgen Lake - A Dry Fly Fishing Primer - by yellowstoneflyfishing.com
(video) The Gulpers of Hebgen Lake - Catching Big Trout During the Callibaetis Hatch | Fly Fishing Waters - by Fly Fishing Waters