how to change negative cable on chevy cobalt

A thorough cleaning should be sufficient to solve the problem at least temporarily. First of all wear old clothes and proper eye protection. You're dealing with sulfuric acid which will wreck your clothing and burn your eyes if you're not careful. Take the connection apart and use a solution of baking soda in water to wash and dissolve the corrosive buildup on the battery terminal and cable end. An old toothbrush and or a small wire brush will help. A light coating of grease will help before reassembling the connection and won't hurt electrical conductivity. If the cable end has deteriorated too much you should be able to buy just the cable end at an auto parts store to replace yours without replacing the entire cable. The type of corrosion you're talking about seems very odd to me. My cable connections are shiny and new looking. Do you have the correct properly vented battery for your car? That's important too.