Very few "regular folk" actually ever got a "legal" divorce because it was costly, and took so much work to attain. More often than not they just walked away from each other and pretended the marriage never happened (my grandmother's father seems to have had that arrangement with his first wife - married 1891, who went on to marry another man - 1902 - after pretending she was the spouse of yet ANOTHER man in the 1900 census for Michigan. She was a plucky thing. Depending on the location and time period they may also have just made a statement in the newspaper, or - and this is a good one - men sold their wives so they didn't have to care for them any more. Sometimes a man would be happy to turn his wife over to another man, and would even sell her for a paltry sum. Google "Poor Man's Divorce" for a few fun sites and descriptions. I remember reading a case where (approx 1825) a man had written in the paper about how awful his wife was, the things she had done wrong, and how he wanted to divorce her right away (basically). In an unusual turn of events the wife responded with a very public description of the man's lack of prowess, and how she was much better rid of him. Yeah, I laughed.
Don't forget to look at all records - even side records like the marriage of children written up in the paper; deaths of others in the family; wills; census. If you can't find the information one way, go in sideways.