My Takamine acoustic has a tendency to buzz when I play the high e string fretted around frets 2 and 3. I figure it's something to do with the neck and tension rod. Are there any other parts of a standard acoustic guitar that can be adjusted to fix string buzz? What's a safe procedure for adjusting the tension rod? Is there anything else that could be causing the buzzing?
Buzzing is almost always caused by a string vibrating against a fret. This could be due to a worn spot on the fret you are pressing on, which results in the string being lower at the point of fretting and higher, unworn frets being in the path of vibration. Finding out which fret is the culprit can be done with a straight edge, but I recommend that you take your guitar to a luthier for a look see. Those guys are professionally trained to spot issues like this, and nearly all consultations are free (at least with the one's I know).
Considering the truss rod, I wouldn't monkey with that. There's a lot of information on the web about how to adjust those, but there's a really good chance you could warp the neck if you don't know what you are doing.
Also, a mis-cut nut, action that is set too low, or playing with a heavy hand can cause these types of buzzing. If you are a hard strummer, consider dealing with the pain of higher action for less buzz. It's a trade off we all have to manage.
Could be caused by a high or low fret.
I had exactly this problem a while back, which I suspect was caused by the nut bedding down a bit. I sort of fixed it by changing my string gauge so I now have slightly heavier at the bottom end (56 instead of 53 if I remember rightly). The higher tension has pulled the neck up just enough to clear the buzz.
I should say that I did this to get more bass out of my acoustic (it's a narrow body) rather than to fix the buzz, but it sorted both.
Obviously, this is not a proper fix but an interesting little anecdote. (Maybe?)
Jduv is right, go and see a luthier or experienced guitar tech. Don't go fiddling with the truss rod!
Regarding the truss rod, lots of people say not to mess with it. However, if you read up on what it does and have a minor adjustment to make to correct high action or fret buzz by low action then a making a couple of half turns the correct way followed by tuning and checking the action is simple enough. Though i must admit the first couple of times i needed an adjustment i went to a guitar tech and watched what they did to build the confidence to tackle it on my own later on.