Is it definitely fret buzz, or is it more of a loud, hollow rattling? If it's the latter, it could be that there's no tension on the truss rod. Try tapping on the back of the neck with your knuckles to see if you can hear the rod rattling.
Assuming it's fret buzz, there may be no relief in the neck. Try putting a capo (or an elastic band

) at the first fret, hold a string down at around the 15th-17th fret or so, then look to see if the string is clear of the frets in the middle of the neck.
If there's a tiny gap, that's neck relief. If there's no gap at all, the neck is perfectly straight or there may even be a bit of a back-bow. Some people like a perfectly straight neck, others prefer a bit of relief to allow room for the greater movement of the strings in the middle of the neck.
Slackening the trussrod
slightly (no more than a quarter-turn anti-clockwise) will let the string tension pull the neck up a little, creating some relief. But be very careful!