The best way to get a 'feel" for what Tenkara is all about is to watch ALL of the videos on the TenkaraUSA website. They're pretty short, and cover everything from setup/takedown, to casting techniques, to fishing smaller and larger waters.
This method of fishing isn't anything new or earth shattering, but it is simple and enjoyable. By Western style gear, I meant a rod with guides, reel, fly line, and leader. With Tenkara, you have rod, leader, and fly. Less equipment to deal with, so you spend less time tinkering with gear, and more time concentrating on your surroundings. You can't cast 40' - more like 20-30'. The rods feel a lot like a very soft bamboo rod in action. They're also extremely sensitive, especially when nymphing with a level line. A 6" fish feels like a whale on the end of the line.
Maybe that's what I find so appealing about Tenkara. The stealthy approach needed to get within casting distance, the delicate presentation, keeping the whole line off the water except for the fly and maybe a bit of tippet (no drag!) - and when you do get a fish on, it's a battle! Small fish are generally easier to find and catch than larger ones, so this technique makes EVERY water you fish trophy class water. Waters often ignored by others become your personal honey holes. The same kind of enjoyment you get from battling a fish on a bamboo rod is magnified even further on a Tenkara rod. Even chubs become fun!
Dapping is something that can be easily done with a Tenkara rod, but it's not the only way to present a fly with them. Many of the casts you do with a "normal" fly rod can be done with a Tenkara rod. By using a longer leader (like a level line 1.5 times the length of the rod), you can cast out further for larger waters. Of course this complicates landing a fish - you wind up hand lining the fish in for the last few feet.
The hardest part about Tenkara fishing is figuring out what to do with your non-casting hand. Takes some getting used to.