I'm not sure about my paternal grandparents (probably through church) but Mom has told me about how her parents met, as well as how her Dad met my step-grandmother.
My maternal grandmother was working in town at the cigar factory. (This was in the early 1910s.) One of her co-workers was one of my grandfather's sisters. One day as they were walking home from work, they dared each other to have their fortunes told by a woman who lived along the way. The fortune teller started with my great-aunt then came to my grandmother. She looked at my grandmother's palm and refused to tell her anything. But grandmother encouraged her. The woman said she would marry and have 2 children, but would not live to see them grow up. She then took a piece of paper and placed it in my grandmother's hand and rubbed her fingers over it. The image of a young man appeared. She said my grandmother would meet and marry this man. My grandmother didn't recognize it as anyone she knew, but great-aunt said he looked like her brother. As they walked on home, my great-aunt saw a young man on the corner and exclaimed "That's him! That's my brother!" It just so happened grandfather had come into town that day. They were married and did have 2 children (a still born son and my Mom) and grandmother died in 1940 when Mom was only 11.
Not long after my grandmother died, Mom and grandpa drove to Missouri to see her relations. My grandmother's sister introduced her friend to my grandfather and they were married later that year (1941). Step-grandmother was a registered nurse and the head of nursing at a St. Louis hospital. One of her perks was a furnished apartment with maid service. She gave it up to live in a farmhouse with only one modern convenience - electricity (installed so a refridgerator could be used to chill medications my grandmother was taking). I asked step-grandmother why she gave up her career and the maid service to be a farmer's wife and a step-mother and she simply said, "Love makes you do strange things".
Mom and Dad were introduced by their parents. It just so happened my grandfathers had both worked at the same company!! Mom was not looking for love having been burned by her first husband (left her to tell his mom he got married and never came back). But my Dad quietly persisted and eventually proposed by asking to adopt my sister. (He also got a cat in the deal.