There are many different ways I have heard this hatch described. Some people call it the "floating carpet" of bugs while I have also heard it called "the blizzard" hatch. Both descriptions are correct in their description of what you witness with this awesome occurrence.
When does it happen? In my 20 years of living and guiding in the Bozeman area I have seen this hatch explode every week of May. This is not a hatch that you can set your watch by. One of the major factors you can follow that will trigger this hatch is water temperature. For these caddis to explode you need the water temperature to be 52-54 degrees. On average, the outdoor temperatures in the Bozeman area is 65 degrees with lows in the mid 30's. A very pleasant weather pattern where the rivers warm gradually and remains fishable until late in May. We sometimes experience a day or two that melts the snow pack at an accelerated pace and may cause some clarity issues. On waters such as the Madison you usually won't have a major problem with run off during this hatch due to the dams helping clean up the water.
What flies do you use? You will need a variety of flies to have success for this hatch. We use dry flies, nymphs and soft hackles. During different times of the days will require different tactics. Generally we start out under the water's surface. We either fish a dry with a dropper or a two fly nymph rig under an indicator. As the day and water heats up and the caddis start emerging, we will switch over to one or two dry flies. When the hatch is in full swing it sometimes becomes impossible to compete with the naturals. With the millions of the real adult caddis on the water it can be difficult to find your fly on the water or present your fly to a trout as they are literally going crazy gorging on spent and egg laying caddis. One of my favorite ways to fish this hatch is with a soft hackle. Casting just above a pod of trout feeding, I will let my soft hackle swing through a group of feeding fish. You will definitely feel the "take" when a trout grabs your fly. No need for a strike indicator, the moment your line stops you will feel the trout. Some our favorite flies I like to use are Nemes soft hackle mother's day caddis, Lafontaine's sparkle pupa's and E/C Cutter caddis. A royal trude is also a great fly for this hatch as it is much easier to see among the naturals than a elk hair caddis or more specific patterns.