Usually all it takes to eliminate these eye sores is a slight shift in your camera angle. Moving in close to your subject will help here, too. Forget you ever heard that. Much more pleasant results will be yours if you just put your subject in the shade, or turn them around so the sun is at their backs. No scrunched-up faces, and much more flattering light.
Overcast days are also good for people pictures.
Take your pictures in the very, very early morning or the very late afternoon. The more pictures you take, the more likely it is you'll get a pleasing photograph. So, use as much film as you can afford. And, when you receive prints back from the developer, don't be afraid to crop them with scissors to achieve your desired effect. A great way to learn about composition and lighting is to look carefully at the works of great photographers.