I think Mary Tyler Moore's hair is a flip with a bouffant. Here is a tutorial that looks good: http://www.youtube.com/watch?v=aA05I5QaZnM
My mother thought I looked really good with a flip in my hair when I was younger and she teased it once (bad, bad, horrid mistake on my hair). That tutorial looks a lot like my mom's technique. I have to imagine that how my mom did it was how they did it in the 60s.