They'd have to be educated enough to read and basic arithmetic. Scavving seems to still be a common enough profession, and knowing what those signs with the guy and a jagged line say is pretty darn important. And arithmetic for... well, you know. Just about anything, since it's that important to know how much of X you have left if you use Y of it.
Even then, unless things have drastically changed, farming isn't as much as you seem to think. Winter and Summer tend to be the "off" seasons, when you're neither planting nor harvesting much. Other professions might need constant work- ammo makers and whatnot. Even then, an ammo maker needs to have some level of education to know how to measure the ingredients to get a consistently deadly enough bullet.
Plus, depending on where you are, you can still get an education. There was an education system in place during the 1800's, which is the general level of the NCR. Having groups that are remnants of various national institutions nearby, as in FO3, can also help. Might end up like Abraham Washington, but the fact that he knows names and a (very) rough idea of what happened is pretty damn impressive considering the circumstances.
And there's still plenty of tribals, such as the White Legs, Sorrows, and Dead Horses, seen in Honest Hearts, that have fully regressed to a pre-modern state, and therefore have no real education to speak of.