Which is correct?
1 Three day's work
2 Three days' work
3 Three days work
I would probably guess (2) is right, since the work belongs to the three days ("three days of work"). But I'm not sure. Would it be different if it was only one day?
"Three days' work" is correct.
Yes, it would be different if it was one day: "one day's work" refers to a single day, so day would not be plural to start with.
It's "three days' work" because of the fact that there are three days. As this is a plural, the apostrophe comes after "s" to distinguish it from a singular, which has the apostrophe come before the "s":