For searing meats, use a frying pan. They have short sides so that steam can escape and you can get a good sear (browning) on your meat. Too much steam will hold liquid in the pan and cause boiling. This means that your meat won’t have enough contact with the hot pan surface and it won’t brown. This is the same reason that it’s important to be careful not to crowd the pan. Too much food in the pan can also cause boiling because there are too many juices running from the meat. Again, your meat will not properly sear (brown).
For roasting in the oven,use a large pan and leave space around your food. This will allow the heat to reach all around it and it will brown evenly.
For cooking in liquid (braising), use a heavy pan with medium high sides (like a Dutch oven) and cover it. This will keep the liquid from evaporating and contain it around the food so that it assists flavoring and simmering. Use just enough liquid to surround the meat so that it will flavor the meat and cook it gently.
For making a reduction, use a pot with a large surface area — one that is wider than it is tall. Spreading out the liquid exposes more of the surface liquid to the air and it will reduce faster. Note that liquids reduce slowly at first and more quickly as time goes on. Therefore, you need to pay close attention as you have less and less liquid. If you are not careful, you can not only totally boil your liquid away. Not only will you have no product left, if you leave it unattended long enough, you can overheat your pan and catch it on fire!
For making stock, use the opposite type of pan that you would use for a reduction. You want the liquid to simmer but not boil away (reduce), so use a pot that is taller than it is wide. Less surface area is exposed, so the liquid will not boil away as quickly.
For melting products (like chocolate) that can easily burn, use a double boiler (two pots that fit together). The bottom pot contains water (just enough so when it boils the water does not touch the top pot) and the top pot sits on top, just above the water. This causes a very gentle heating process that insulates tender products and protects them from burning.
The same is true for baking tender things like custard in the oven. You can cook them in a water bath by placing the cooking vessels on a jelly roll pan (cooking sheet with sides) or larger pan with sides and then adding just enough water to come about half way up the sides of the vessels containing your custard.
For steaming, use 2 pots that are almost exactly like a double boiler, except that the top pot has holes in it to allow the steam from the boiling water to come through and cook (steam) the food. Generally, use a pot that is several inches taller and wider than what you want to cook. If your pot is too large, you can burn your food. If it’s too small, it can overflow, so choose the size of the pan according to how much food you want to cook.
Don’t forget to allow for food that grows in size as it cooks, like rice (which triples in size) and caramel corn sauce (which bubbles up when the soda is added).
No matter what pan you are using, remember to stay in total control of your heat. Pans with heavy bottoms will help, but it’s up to you to cook food steadily and carefully so that it won’t burn. Have fun!