The ingredients in the sunscreen can block UVA and UVB rays either chemically, or physically. A chemical sunscreen must be applied at least 30 minutes before exposure to the sun. Look for is avobenzone. For people with more sensitive or delicate skin, I suggest using a physical sunscreen. This is an ingredient that, when applied to the skin, provides a physical barrier that the UV rays can't penetrate.
Zinc oxide is a wonderful physical sunscreen.
A cousin of zinc oxide, and a marvelous 21st century ingredient, to look for is called titanium dioxide. It's fabulous on the skin, is non-irritating and won't clog pores. The common drug store sunscreen products are usually fine for use on the body, but for your face you should look for products that contain these ingredients. Keeping your skin clean and exfoliated is the key. Use either a foaming gel cleanser or a clay cleanser if your skin is very oily.