
Oil should be heated to the correct temperature before cooking. When you put food into oil, it should sizzle (have little bubbles or make a crackling sound). One way to tell your oil is heated is to lift the pan a tiny bit and look for ripples in the oil. Some have suggested splashing a couple drops of water in and see if it splatters. After a while, you'll be able to tell just by how easily the oil swirls.
If you have non-stick and are trying to ease up on oils, a spray is fine, but you won't get the same influsion of flavor or crispiness in certain foods. They sell oil sprays and spritzers, or if you don't really care about health and aerosols, there's good ol' Pam.
I have actually used bacon grease or lard in the distant past for flavor, but go with olive oil and a lighter cooking oil otherwise (palm, coconut, walnut, peanut, safflower, grapeseed, or canola). I mostly go with olive for Italian, Mediterranean, or light American meals and mostly the lighter oil for everything else. Many nutritionists recommend grapeseed or coconut. Grapeseed is fairly pricey and coconut leaves a hint of its flavor in your food, which my family didn't like. I discovered that canola oil is genetically modified and can hurt the environment. It's amazing how we try to progress, but what our grandmothers used was probably the best for us.
I use olive oil to sautee dark greens, roast red potatoes, or for salad dressings. It goes nicely with coarse salts (sea salt & kosher salt). Lighter oil seems to be better for white, gold, yellow, or russet (the regular brown) potatoes. For deep-frying, which I don't do often, peanut oil is good. Something common to Chinese cooking is to "season" a stainless-steel or iron wok with peanut oil the first time one uses it. Seasoning just means dipping a paper towel in the oil and then rubbing all around the inside of the wok. You do something like this with cast-iron skillets as well.
Extra Virgin Olive Oil. Don't go for blends, "light" olive oil, or even "natural" olive oil, particularly for your salads or simpler foods. Go with "Extra Virgin" for quality and taste. As for the brand, I have a certain fruitiness I like in my olive oil. Use whatever you like. Just look to keep low on saturated fats and don't buy anything with trans fats.