The act of stripping your line/fly is most often done with just one hand doing the pulling. This is often very effective because you'll always have one hand firmly on the rod handle and the other firmly on the line, so when a strike comes you'll be in a good position. In addition, the pause between strips can give your fly increased action and may help trigger a bite. But, what if you want a more consistent retrieve or just purely more speed? You can single-hand strip as fast as you can, but the fly will always stop between pulls, albeit briefly. The "fix" is an easy one: use both hands!
After the cast is completed, simply wedge the rod handle under the armpit of whichever arm you prefer. If the wind is from the side, I like put the rod under the arm that's on the downwind side of my body. Make sure that the reel is free and clear behind your armpit, not under it.
With the rod tip pointing down at the water's surface (hunching over helps), simply use one hand to grab the line at the first stripping guide and pull down in a typical stripping motion. I like to strip the line off to the same side of my body that I'm holding the rod on. So, if the rod is under my right arm, the loose line is being directed to my right side. This keeps the loose line out of the way and not laying across my feet/legs where it could more easily tangle or get stepped on.
Just before you reach the end of that first stripping motion (however long you want it to be), bring your other hand up to grab the line (at the first stripping guide again) to continue the stripping motion without a pause. Don't let go of the line with the first hand until the second hand has taken over.
Hookset: When a strike comes, it can be a bit awkward the first few times since you're not actually holding the rod with your hand. If a fish eats, simply continuing to strip until you feel the fish is solidly hooked can work well. Other times, using longer, firmer strips or jabs to set the hook can be effective on bigger fish. After the fish is stuck, I keep a hold of any uncleared line (letting it slip through my hand if needed) while quickly grabbing the rod handle with my dominant hand to fight the fish as usual. As I make that transfer, I sometimes like to angle my body/the rod a bit to the side (which puts a bend in the rod) to help absorb some of the shock.
Why: As mentioned, this technique gives you the ability to retrieve the fly non-stop and/or at a rapid pace. Of course, you can still stop the retrieve at any time to let the fly sink or pause. Using the two-handed strip also makes it easy to change the swimming action of the fly. Just like with an artificial lure like a plug or spinnerbait, you can constantly spice up the retrieve by just slowing or speeding up your stripping motions and even further mix it up with an abrupt tug or twitch here and there.
When: Some saltwater fish like tuna and striped bass may favor a very fast retrieve which this technique is tailor-made for. However, two-handed stripping can obviously be used any time you want to use a steady retrieve. For example, if you're a stillwater trout angler, you can incorporate short, slow pulls to maintain precise line contact and steadily crawl your fly through the water.
Also: Not just for actually fishing the fly, stripping with two hands is a great way to rapidly bring in excess line if you need to make a quick recast or if you need to pull the fly in after it's been fouled. It's a real time saver!