Always read the labels. You probably learned how to read labels in a basic health class when you were in high school. You also probably didn't care about because you were going to eat whatever you wanted to. Sure, you might have checked the fat content or the number of calories per serving. There is so much more to it than that.
Be careful about products that say "processed on shared equipment" or "manufactured in a facility that also processes wheat." For someone like my son who has celiac disease, these products are not allowed. I might consume them because a small amount of cross-contamination won't hurt me. (If I were to ever get something that had been heavily cross-contaminated, however, I would experience abdominal pains.)
Labels must tell you if they contain any of the eight most common allergens: milk, soy, egg, wheat, tree nuts, peanuts, fish, and shellfish. Always look for wheat. If it says that it may contain it, don't even try it. You must still check all of the other ingredients. Sometimes products will say "Gluten-Free" under the list of ingredients. It can only say that if the company has tested the product and found that it contains less than 20 ppm (parts per million) gluten.
Unfortunately, there are some products that say "Gluten Free" on the front of the package but then say "manufactured on equipment that processes wheat." Again, READ THE LABEL!