It's not just the fat, it's also the heat. Know what you're cooking and how. Some things will burn no matter what if the heat is too high, and some will get greasy if the heat isn't high enough.
You can also get soggy/greasy food if there's too much food in the pan, or if it's a very wet food like mushrooms or a protein that wasn't pat dry first. Liquid is your enemy; it will generate steam which will make everything go wrong.
If you're using a small amount of oil and the food burns, your heat is likely too high. Very high heat is usually used for quick cooks like a stir fry, or to finish off a sauce. Try lowering your heat.
It'd help to know more about what you're cooking and what your results have been. Then we can nitpick at you. :-)