Vinegar works great to remove stuck-on grease and burn marks. White wine vinegar is what I usually use. Put a mix of about 1 part vinegar to 3 parts water in the pot, let it soak for an hour or so, and it should really help. For the bottoms of pans, good old fashioned steel wool, like Brillo pads, is awesome. Keep in mind, though, it is very abrasive, so don't use it on anything with a non-stick surface or on pots with enamel coating, or you can ruin the surfaces. I use it strictly for the bottoms of pots.
Your best bet would be to soak your pot in soap and water. Let your pot soak for at least ten minutes depending on how bad it is. You then take a sponge that has a scrubby end on it and scrub the burnt food off. If that doesn't work soak the pot longer and repeat the process.
I'd like to add that the combination of baking soda and vinegar can work miracles from the fizzyness that results from mixing the two ingredients. Clean any roasting pan by sprinkling the surface well with baking soda. Combine 1 cup of hot water and 1/3 cup of vinegar, poured onto the baking soda. The fizzing action will remove the roasted food particles.
To get burned food out of a pot the best way is to first remove as much as you can by hand. Next pour baking soda into the pan and enough water to cover the bottom and bring to a rapid boil. Allow the pot to soak. You may have to repeat several times in order to remove the burned food completely. Tip: If you are using non-stick cookware, you can always spray with a non-stick spray to prevent food from sticking.