Remove the old bar tape and the end caps from the handlebars. They should pull out with your fingernails. Remove the brake/shifter combination from each side of the handlebars.
My brake/shifters are made by Shimano. To loosen and remove, peel back the forward edge of the rubber covering on the outer side about midway between top and bottom of the rubber. You will see a bolt head for a hex key wrench at an angle outward. Loosen it until you can slide the brake/shifter off of the end of the handlebar.
Clean the bits of old adhesive from the handlebars. Gently twist each piece of noodle into position on the handlebars. It is possible to be too aggressive and get a linear rip in the material. Saw it to its approximate length with a sharp knife. Slide the brake/shifters into place after the upper portions of noodle are in place and are cut to size. Eyeball their position so both are at the same height on the handlebars.
I did not try to feed the brake cables through the inside of the noodle sections, but taped them on the outside of the foam grips. I tried to place them so they would be under the bends in my fingers. I had bought some colored tape at Radio Shack for some project a long time back. The roll of orange tape came in handy here.
I taped each end of each grip. The end caps were loose, so I wrapped about two turns of vinyl electrical tape around them and pushed them into the ends of the handlebars.
I tried the new foam grips out on a 28 mile ride. They hold up well and are very comfortable. My hands did not even begin to numb.