I am also approaching my 70s and find some aspects of DNA very difficult to get my head round. I fear it has come too late for me to get full value from it,, but hope my daughter, currently uninterested in family history, will gain from both of her parents being tested.
I took no interest until in my 50s, so there's hope yet.
You say you will need leading slowly - it is only by taking an active interest in the subject that you will learn, and you are doing so. The mud becomes clearer after a while, but not completely clear for me as yet!
Wrong side of the blanket does immediately spring to mind, so tread carefully.
As I said before, shared matches should give you a lot of information.
Depending upon the age of your match, you could be looking at a number of different generations.
Gadget says most likely relationships include Great-Grandparent /Great-Aunt / Uncle Half Aunt / Uncle 1C/ Half Niece / Nephew /Great-Niece / Nephew /Great-Grandchild, from DNA painter.
So, given your age, not likely to be your great grandparents, or even your great aunt/uncle that the match shares.
Match is more likely to be your great niece/nephew or your great grandchild etc.
If the match is about the same age as you, consider closer relationships, nephew/niece
Whichever way, it is probably either yourself or your parents the likely common ancestor.
Regards Margaret