The first step in removing the odor of burned food is to open the windows; this lets air circulate. The fresh air comes in, helping the burnt smell fade away. There are several other options that move the process along. A burnt smell is typical when food is seriously overcooked.
Simmering cloves on the stove puts a pleasant smell into the air. One-half cup of whole cloves in a heavy saucepan with two cups of water does the trick as it is warmed on a low flame for 15 to 30 minutes. The burnt smell will be replaced by the aroma of spice. Another option is a can of commercial odor reducer that sprays into the air. It is possible to make a homemade spray version with fresh lemon juice in a spray bottle.
Another natural remedy for removing a burnt smell is baking soda. Placing a few small bowls of baking soda throughout the rooms that are affected reduces the odor. This is a slower process, but it requires little effort. If the burnt smell is coming from the microwave, citrus fruit freshens both the appliance and the air. One cup of lemon, lime or orange juice with one cup of water or cut-up piece of citrus fruit in water heated in the microwave on high creates steam that takes care of this odor.