So, 21 yo mountain bike w/o quick release brake system. Reinstalling a front tire that was repaired but confused on easiest/simpliest way to release brakes so the fat 'ol tire can be seated. I do realize I can deflate the tire but wanted to learn another method. I don't want to create a mess by going at it w/o a bit of guidance - any help would be most appreciated
The intended method is to unhook the cable from the far cantilever in the photograph. Hopefully the straddle cable end fitting has a wedge-shaped bit sticking out of the back of the calliper, as visible on the far left here: . Squeeze the two brake arms together, and pull on this wedge, and lift the metal cylindrical part out of the slot. If there is no wedge shaped piece, push the cable into the caliper to free it. Some straddle cables have a piece of metal on the cable to help you do this but I can't see one in your photo. There is video and pictorial explanation here: http://www.madegood.org/bikes/repair/open-a-cantilever-brake/
There should actually be a quick release option with those older cantilever brakes. On the caliper on the left (if you are looking directly at the bike from the front) where the straddle cable attaches to the caliper is a small metallic object connected to the cable that you can pull out of the caliper. This will release the brake so you can remove/ replace the wheel.