One of the most "packable" ways to fish for trout is using a tenkara rod.
Tenkara the traditional Japanese method of fly-fishing where only a rod, line and fly are used.
Tenkara may have originated in Japan but its becoming very popular amongst anglers looking for fly-fishing simplicity and mountain-stream effectiveness.
Eleven to fourteen foot long rods allow anglers to fish mountain streams in a way that is nearly impossible with western fly gear.
Telescopic rods collapse down to a mere 20 inches, and few things are needed making tenkara ideal for backpacking.
outdoors.stackexchange.com/users/350/ssduplantis
I like to fish trout with sweet corn.
They seem to like it and it comes in small cans.
Bringing a roll of fishing line and some small hooks should be enough.
You can roll up the fishing line on a stick and make your own swimmer out of some light wood.
At least this worked for me.
It doesn't give you a bountiful yield of trout but should suffice if you want to keep your fishing gear light weight.
outdoors.stackexchange.com/users/105/Thomas Rawyler
I really hate to mention Walmart
but I saw a collapsible rod for gear fishing there that collapses down to about 16" and extends to around 5'.
It was really light
and I think it cost about $20.
I had one of these a while back
and it worked great on hikes.
At $20 I felt comfortable taking it out hiking without the fear of breaking it.
You'll also need a lightweight reel, a couple small rooster tails, and a hook.
Use what ever bait and weight you can find in the environment.
Trout love grasshoppers and beetles.
Usually mountain lakes are small and have smaller trout in them
so you don't need anything heavy duty.
Tenkara is great for streams but I wouldn't want to fish from the shore of a lake with one.
outdoors.stackexchange.com/users/2452/stuckintheshuck
In addition to ssduplantis's mention to Tenkara, I would like to write that some fly rods are very portable.
Some manufacturers make rods consisting of up to 7 pieces, which fit into a 40cm canister that is very portable.
One example is the Orvis frequent flyer series .
That, a fly reel, a box of flies, and a leader would not take much more space than a Tenkara rod.
I personally own a 8 wt 9ft of these rods and am very satisfied with it's quality.
outdoors.stackexchange.com/users/3660/Kenji
Matthew Perry on Quora writes: There are many four piece rods that will work.
I even have a five piece by TFO that works good too.
I usually use it as a backup rod.
You want to have two rods in case you break one.
Nothing worse than hiking in a good distance only to break a rod.
Been there done that.
outdoors.stackexchange.com/users/6387/RV Park
Several of the places we hike every year have trout.  I'd like to have some fresh fish on a couple of those hikes but I'm pretty new to trout fishing and I don't want to carry the weight of full fishing gear.  What type of pole would be best for a portable trout fishing setup?
What type of pole can be used for trout while backpacking?
outdoors.stackexchange.com
<backpacking><fishing>
outdoors.stackexchange.com/questions/388
outdoors.stackexchange.com/users/127/Russell Steen
S0: One of the most "packable" ways to fish for trout is using a  tenkara  rod.      A tenkara rod can be used.
A tenkara rod can be used.