The Tolkien Gateway says they were "herdsmen and farmers".
Tolkien described them as "still partly mobile and nomadic people of horse-breeders" (Letter #297), so I guess they at least became partly settled. But the only description I can find of their farms and crops in the books is:
Where is the spring and the harvest and the tall corn growing?
Thus spoke a forgotten poet long ago in Rohan, recalling how tall and fair was Eorl the Young, who rode down out of the North
-- The King of the Golden Hall
Apparently they were used to farming even in the era of Eorl.
Are there more descriptions of the economy of Rohan? Their villages, their crops, their diet?
Some context for "partly mobile and nomadic":
Rohan. I cannot understand why the name of a country (stated to be Elvish) should be associated with anything Germanic; still less with the only remotely similar O.N. rann 'house', which is incidentally not at all appropriate to a still partly mobile and nomadic people of horse-breeders!