If food is stuck and difficult to remove, then you should soak the dish in a mixture of dish detergent and warm water. The food will loosen quite quickly (i.e. in 30 minutes max...while you eat). In most instances, this method will do the trick. If a dish looks like it is going to be really hard work to clean, then do not let it go cold before you take action, because then the residues stick even harder.
If a dish or pan has cooked or boiled dry with food in it, it may be harder to remove. For this problem, a good method is to cool it a little, then fill it with a solution of powder laundry detergent, such as Tide, and warm water (approx 2 teaspoons in 2 pints water). This powder has enzymes in it that help to dissolve grease and residues (this solution, in greater quantities, is also "the best" for dissolving grease on oven racks or barbeque grills). For pans, you then boil it on the stovetop and simmer for a few minutes. Finally, empty the liquid into the sink. Repeat again if necessary.