As suggested, deglaze with water to soften any residue and then let it soak. Then scrape with a plastic scraper (e.g., the plastic spatula) and then clean with a dishwashing brush or nylon scrubber. Use a blue 3-M (non-scratching) sponge for stubborn spots (but not green, which will scratch the pan.) Then polish with copper cleaner (I use Wright's, but Twinkle works well, too) to remove heat discoloration and hard water deposits, and polish the surface. Cooked-on spots can be softened with a paper towel saturated with ammonia, leave the soaked towel on the spot for 10-15 minutes. To avoid scratching the pan, I try to avoid using any pumice-based cleaners like Bar Helpers, Bon Ami or Ajax. (I just tried using bathroom tile cleaner, and it also worked to remove hard water deposits.) If your pans have an anodized aluminum exterior, try to avoid using oven cleaner or anything with lye in it.
If you pan has an aluminum core, don't leave the lid on when you are soaking the pan or soak cooking utensils or flatware in the pan overnight, since it will cause the aluminum edge to oxidize. If the aluminum edge is getting discolored, you can polish it with a tiny piece of SOS pad, being careful to avoid scratching the exterior surface of the pan.
Whenever possible, I try to avoid using metal utensils in our SS pans (exception: the balloon whisk I use for making sauces.)
Most of our All-Clad still looks almost like new after 25 years of regular use.