I have been backpacking all over the sierras around the JMT for years, with the main reason being to fish. You can fish juuuuust about anywhere along the route as long as you have a California fishing license.
As far as the type of fish…you will catch only trout. Brown and rainbow trout in the lower elevations, brooks in the middle elevation (7,000 and up) and there are golden trout in the higher elevations (above 9,000) in the southern parts of the trail. There will be trout in just about every stream and lake….some better than others. You will know if they are there…you can see them, and at sunrise and sunset they feed on the surface and you will see the rings on the water they make.
It is not unusual to catch several dozen fish in a day if you are trying and in the right spots. The average size of a trout you will be catching is around 6-12 inches. The higher the elevation, the smaller the trout…typically.
I would recommend a Shakespear 4'6'' telescopic rod. Like this
http://www.amazon.com/Shakespeare-Travel-Casting-4-Feet-6-Inch/dp/B0000AUWG3
Its really light weight and packs small. I get a small cardboard postal tube from the post office and it fits the rod perfectly to protect the rod.
Match that with the smallest spinning real you can find, and put no more than 4lb test on it.
I use flys with that set up. If you get a bubble that you can fill with water and then tie a barrel swivel with a 3ft leader. Use a size 14 size fly. My favorite is a tan elk hair cadis.
The fly is good because it is single hooked, not a treble (triple)hook. its easier to get out, and they dont swallow it so you can easily throw them back if they are too small or ya just wana have some fun and do catch and release.
Fill the bubble with water…the more water, the more weight the further you will cast. So fill accordingly (stream vs lake).
Whatever you wana keep just clean and cook directly on the fire. I like to get a hot bed of coals going….lay a row of sticks (each about a quarter inch thick) on top of the coals. Cook the trout on both sides till the skin chars. If cooked right the spine and all the bones will just peel out like butter.
Hope that helps a little. PM me if you have more questions