Important note: not a man. But, hey, I know some. So this is what happened for those who come to my mind first.
My husband: we met on Quora. I promoted one of his answers back when they had that function. He thanked me, we became FB friends. Couldn't meet him in person to hang out based on our shared interesr because his weird girlfriend at the time sent me messages disallowing it (which he knew nothing of, but I assumed he did and stepped back since I don't need friends with crazy jealous partners). They broke up for unrelated reasons. We hung out in person. Friends in person for a couple years. Eventually we both realized, "Holy shit, we've been talking to each other about everything and discussing relationships, but WE should be together. We are so compatible... AND now we realize we turn each other on." It started the night he came over to watch a movie at my place. He saw my messy kitchen and cleaned it for me even though I felt embarrassed (I had been depressed and not so great at cleaning), and then he hugged me and finally smelled my hair for real for the first time (pheremones, yay!), I could tell he suddenly felt attracted in a way he hadn't before and so that turned me on, and then a day later he asked me out and explained what had changed in his thinking about me, and how. I said yes. (He says he always knew I was pretty before then, but he's in his forties and used to finding women pretty without also wanting to be with them... and then he first smelled my hair he thought, "OH, FUCK.")
We were friends for two years and now we have been together romantically for two years.
A friend's husband: she divorced her former husband because the former husband cheated, and this guy's wife had died a few years earlier. These two had gone to high school together. They had a chance meeting while out and agreed to get together. They did get together, they fell in love, and they married.
They have been together romantically for four years.
A relative: they met at work after horrible earlier marriages.
Their marriage now seems to be awesome after, oh... ten years?
PS: marriage obviously isn't necessary for or required of love. These were just the first three things that came to my mind. My real answer to how people over 30 meet partners is too broad though: all sorts of ways.
PPS: I just remembered another relative who met her husband when she was 60 And he was 68 by meeting him at a social gathering. They were together 23 years until he died.