Feelin' Groovy Man.. Wanna smoke a ----?
Actually I grew up in the late 1960's and whole decade of 1970's which were a lot like the 60's. I thought it was a great time to grow up. People weren't as uptight as they are today. The pop music was ten times better. In the 1960's and 1970's there was a huge explosion of rebellion against culture of preceding decades, most notably the 1930's /40's/ 50's; which were all hopelessly stodgy, racist, conservative ,ridiculous and phony. (Yeah, good ole U.S.A. :\)
Also during this time penicillin was discovered so people went wild and had wild sex with each other all the time since there didn't seem to be any worry about diseases that were once life threatening of disfiguring. We didn't have HIV or HERPES running around like you see now. All the sexual diseases back then were curable.
If the 1940's and 50's weren't ridiculous as I described the children that were born during this time who were adults in the 1960's wouldn't have rebelled like they did. It was huge shift in attitudes and culture.
Oh, to answer your question, people greeted each other much like they do today, except they used slang expressions that would seem silly today, like FAR OUT, GROOVY, etc..