If the offending pan is really bad buy some wet and dry sandpaper and wet the sandpaper and a little soap and sand off then polish with a fine sandpaper very good on burnt copper pans
What I find works brilliantly too is put about 2 tablespoons of biacarbonate of soda into the saucepan with boiling water and leave over night, the black does leave the saucepan
Pour about 1 inch of malt vinegar in blacked out pan bring to the boil and simmer for 20 minutes and then leave to rest on stove for overnight. Repeat process if necessary and you will find it your scrapes away.
Good Luck
Add a laundry detergent tablet (or a scoop of powder detergent) and water and then bring to a simmer. Allow to simmer for a while and it will remove all the burned on food.
Buy a packet of soda crystals, pour a good handful into your pan, top up with hot water and leave to soak for a few hours.
Get a washing up brush and them scrub the pan before washing as normal in hot soapy water.
If your pan is badly burnt you may need to repeat the process
When you realise its burnt, while the pan is still hot, put salt on it, lots of it leave for 10 minutes then put some hot water in the pan and let it soak