I found out about the 11-year cycle in a fun way. I was a teenaged amateur astronomer, and brought my telescope outside in the day for some solar viewing.
No, you don't look through the telescope at the sun. You hold a piece of paper out a certain distance from the eyepiece, and focus. You can see a very detailed picture. (Don't hold it too close to the eye piece, of course.)
The lucky thing for me was that it was the peak of the 11-year cycle, which I found out later. I had a few large sunspots to see.