Part of Tenkara's appeal is the lack of necessary equipment, so here's all you really need for a successful time catching fish.
Tenkara fishing, first made popular in cold water streams in the mountains of Japan
All you need for tenkara fishing
Rod - Clearly the rod is the essential part of Tenkara, and it's worth pointing out the delicacy they can have over Western fly rods. Practice total caution telescoping the rod both out and in your first few times doing it, and pull the sections together snug, and not too tight.
Line - Tenkara line can be either furled or level. Knots and techniques will vary slightly, but go with furled if you're just starting out.
Tippet - Tippet material, to attach your fly to the tenkara line, will be needed. 5x or 6x diameter will do.
Flies - The flies used for tenkara fishing don't have to be all that different that those used in Western fly fishing. A box is helpful, but since many tenkara anglers focus on only a few fly patterns, having no more than a half dozen on you at any time isn't unheard of, nor uncommon.
Line Nipper - While tying (and especially when first learning to tie) knots for tenkara, it's easy to end up with excess line and tippet material. Nippers, or clips, will really come in handy.
Forceps - As much for the fish as for you, a good pair of forceps will make unhooking fish far easier. Don't be the guy who sacrifices a fish he didn't intend to kill because he couldn't get the hook out safely.
And for good measure, here are some things you definitely DON'T need for Tenkara fishing.
Vest - There's really no reason for a ton of pockets and accessory holders. A small pouch or bag will get the job done, as will a small fly box in your back pocket.
Reel - Duh.
Expensive Fly Line - Since the price just keep running up on modern fly lines, this is a welcome relief.
Backing - Needed to fill the reel if a fish takes you for a long run, backing isn't necessary on a tenkara set up.
As you can tell, the amount of stuff actually needed is minimal, which is what draws a lot of anglers to tenkara in the first place.
This way, just about any trip can turn into a fishing trip when you don't have to lug around so much gear.