Well the first thing to do is work out if it's a problem with the lens or the camera.. my gut is that it's the lens and the irises are stuck and I say this because it works fine unless the camera has to "stop down" to a smaller aperture like another poster said.
Take off the lens and find this little tab that I'm pointing to with the screw driver.
It is spring loaded so with the lens off the camera it should be wide open. If you look through the lens and tweak this little lever you should see the aperture irises snap open and shut. If you can't move that lever then this lens is toast.. and honestly not trying to get repaired because it's so plentiful and cheap used.. better still, buy something better!
If it is stuck you've actually nothing to lose by pulling the back off it. It's just a couple of screws. I'd loosen those screws on the back a little until you can get a bit of a wiggle on back plate and see if that unfouls whatever is fouled up on something.
If that's moving fine then it's something else, possibly the part of the camera that mates to it. It's at 9 o'clock as you look into the camera with lens removed. I wouldn't mess with that, although you could give it the lightest push DOWN to make sure it actually moves. If it's NOT at 9 o'clock, more like 8, then that's a problem and the tensioner on it might have gone bad.
That's the point at which I think DIY investigation comes to an end.
If you don't like the look of any of this, find someone else with a Nikon AF lens, and see if the same thing happens - or go to a camera store, tell them you think your lens is bad, and ask to use theirs, and see if it has the same result.