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Its not always that easy. Buzz on the first few frets implies that the nuts too low doesn't it? It's not that straightforward to fill (then file) or shim the nut - raising the bridge might help but then the action changes more.
I'm terrible at setting up guitars - always think it's worth taking it to someone who knows.
edit: assuming no fretwork needed
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fair enough, I was coming at it from a point of view of having set up lots of guitars in the past but appreciate most people wouldn't have done that sort of thing.
should be pretty easy to sort if it is what I think it is. I would just clean/file and fill the groove in the nut (assuming its an open string thats giving the buzz) with packed out bicarbonate of soda and a drop of super glue, repeating until the groove is built up. that will fill up the groove to be rock solid, much like the nut, then file it back to where it needs to be. that would raise the string enough to clear the frets it's buzzing on.
It's an easy job to do yourself. Probably be a tutorial on YouTube