I started by removing the speaker ring that holds the outer edge down and suspends the tweeter. I just unscrewed the tweeter from the back and unsoldered the two wires leading to it. Once the tweeter was removed it was easy to start removing the crumbling surrounds. What was left of the surrounds on the paper cone I removed with a razor and some rubbing alcohol.
When the paper cone and the metal cage is cleaned up you can glue the surround on. I started with gluing the edge of the surround to the paper cone. I ran a 1/8" bead around the edge of the cone and centered the surround to the edge of the cone. I worked the glued edges together for a few minutes.
Once the surround sat about an hour I glued the outside edge of the surround to the cage. Before gluing the surround to the cage, push straight down on the paper cone gently to make sure it`s centered around the voice coil. If you can hear it scrape, then wiggle it one way or another until it moves up and down smoothly. When it does, it`s okay to run a bead of glue under the edge of the surround and work it to the cage with your fingers. You can now put the outer ring over the edge to help hold the surround down.
After an hour I reinstalled the tweeters, soldering the two wires that lead through the woofer cone. When the surround is back on and the glue is set, she`s ready to play. I did both of these in about 1.5 hours complete with changing out two blown capacitors on the tweeters. So don`t throw those old speakers away, they can be saved. This same process can be done with 4 x 10 car speakers or full size 10"-18" stereo and pro audio speakers.