I have been making these little lights for years now with students. They are very easy to make and work surprisingly well. I actually kept one in the glove-box of my car for many years and used it often when rummaging around for junk or coins under the seat etc. Great as a key ring, emergency light in the fuse-box, in a woman's purse or reading in bed perhaps?.

You will need:
3v button cell battery (20mm)
Super-bright LED (your choice of colour)
Neoprene sheet. (or an old Mouse-mat , "Wonderfoam", foam tape)
Thin but stiff plastic (Yogurt container, Ice cream lid etc)
Double sided tape
Scissors
Utility knife
Disk-sander (optional)

Step 1: The Sandwich

step 1
This is basically a sandwich construction with the neoprene mouse-mat as the 'meat' between 2 pieces of plastic.
Roughly cut the center piece of neoprene into the desired shape and mark-out where the button cell battery might fit by tracing it.
Allow at least 5mm from your mark to the edge.
Cut out the hole with the utility knife.
If anything, it should be a little small and a snug fit.

Step 2: The "Bread"

step 2The "Bread"
In this case, I used "Wonderfoam" as the 'bread' for my sandwich. Or in other words, the outside layers of the torch. Cut 2 outside layers to roughly the same shape and 1 piece or hard plastic also to the same shape. This will add stiffness to the torch.

Note:
Alternativaly, thin, stiff pieces of plastic could also be used as the outside layers and therefor there would only be 3 layers in total.

Step 3: The LED

step 3
Bend one leg of the LED. In this case I bent the positive (longer) leg.
I this case, I made a little notch for the LED to slip into so it would not protrude out from the 'sandwich'
If you do this, then the hard, thin plastic needs to be trimmed.
But not the outside layers!

Step 4: Assemble the Torch

step 4
Use double sided tape to assemble the layers.
The straight leg of the LED is next to the hard plastic and the bent leg acts a press switch on the top.

Step 5: Finishing

step 5
Gently sand up the edges on a disk sander. The LED will not break if it torches the sanding disk, it will just get scratched.
In these photos you can see one example with the LED not having a little recess cut in order to protect it.
Both still work really well!
If you do not have a disk sander the I really love THIS Instructable by M.H.Kabi. Could be great little sander and I will be making one myself to find out!