It's simply letting a fly sink (by using a dead drift) and then letting the line tighten to make the fly rise in water column at a spot where there's a fish holding.
In Leisenring's own words:
"Now watch the fly. It is almost to him, and would only have to travel about four more feet to pass right by his nose without his looking at it unless it can be made to appear alive and escaping. At this point the progress of the rod following the fly is checked, and the pressure of the water against the stationary line and leader is slowly lifting the fly."
"The trout notices it. The hackles or legs start to work, opening and closing, and our trout is backing downstream in order to watch the fly a little more, because he is not quite persuaded as yet. Now you can see the fly become even more deadly. As more water flows against the line, the fly rises higher off the bottom and the hackle is working in every fiber. It will jump out of the water in a minute, now, and the trout is coming for it. Bang! He's got it"
It's not rocket science, you probably already do something similar. The trick is to time to make sure the fly rises right in front of a fish.
It's related to Sawyer's "induced take." The difference that Sawyer was fishing upstream and needed to actually lift the rod to get the fly to rise. Leisenring only needed to let the line go tight, not lift the rod.