Many years ago, when I was twenty three, I got married to a widow, who was pretty as could be.
This widow had a grown up daughter, who had hair of red.
My father fell in love with her and soon the two were wed.
This made my dad my son-in-law and changed my very life.
My daughter was my mother, for she was my father's wife.
To complicate the matters worse, although it brought me joy, I soon became the father of a bouncing baby boy.
My little baby then became a brother-in-law to dad. And so became my uncle, though it made me very sad.
For if he was my uncle, then that also made him brother to the widow's grown up daughter, who of course was my stepmother.
My Father's wife then had a son, who kept them on the run. And he became my grandson, for he was my daughter's son.
My wife is now my mother's mother, and it makes me blue, because although she is my wife, she's my grandmother too.
If my wife is my grandmother, then I am her grandchild. And every time I think of it, it simply drives me wild.
For now I have become the strangest case you ever saw; as the husband of my grandmother, I am my own grandpa!
Note that most of the text is expressing all sorts of confusing relationships, but the "heart" of how he became his own Grandpa without any incest or impropriety is simple:
That's all there is to it. He is now his own grandpa. (One would hope that the lady and his bio-father both married at a very young age, otherwise the differences in age between he and his wife and his father and his wife would fall into impropriety.)
Of course, the story teller's METHOD of telling it is much more entertaining!