I teach SUP and work the Naish tent at local paddling festivals. Last weekend near Portland, Oregon due to the beginning to what some call 'paddling season' and warm weather, we had a high volume crowd of folks coming out to take basic SUP lessons and demo boards and paddles. It's great training for SUP instructors as we deal with many different body types, personalities, and skill levels.
I had two guys in their upper 50's and 60's who had bad knees with little or no flexibility in one leg. Wearing PFDs, we managed to get them up standing from the beach. Later in the day Sunday, a woman in her 60's was flailing in the water asking for help. She had fallen off her board, her PFD had slipped nearly over her head, and she said she couldn't swim. As I paddled close to her she was panicking and trying to grab my board but in such a way she would've capsized me. Given we were 30 feet from shore, I was able to have her hold on to my board and drag her to where she could touch bottom quickly. If I were further out, I would do the flip rescue to get on her own board. More on that in future posts.
A few thoughts here.. If you can't swim, take a swimming lesson first, then take a SUP or kayak class. Even with a PFD on your fear of the water may lead to panic or even worse being rescued. Swimming classes are held regularly, and it's without question an invaluable skill to have. By entering the water without this skills, you're also endangering those around you who will need to perform a rescue, hopefully not in open water or rough conditions.
Looking for swimming lessons? Here's a site which can help you find them.. Swim Lessons.