Buzz is of course an issue of string to fret contact.
There are 4 elements to string height. The NUT, The BRIDGE, The NECK's relief (or bow), & the STRING itself; it's composition, size, tension, construction.
Generally speaking a nut is filed at the time of factory setup and has a moderate effect on string height. It can be lowered or raised but the overall effect is less than that of the bridge unless the nut is really screwed up.
The bridge saddles have a large affect on string height. IF the string saddles are all the way down......and you have a buzz; naturally raise them. ANY alteration of the saddles may have an effect on proper tune & intonation but that's another issue.
The neck has a truss-rod that tightens when you turn in clockwise and loosens when you turn it to the left. You can make a neck almost perfectly straight (with no relief) and that may contribute to fret buzz if the strings are too low. "Relief" is the amount of "bow" the neck has generally at the 12th fret. Many players was a tiny amount of relief due to the natural vibration elements of the string which will vibrate widest at the center of the string length.
The STRING itself can be contributing factor to fret buzz. Some string vibrate LESS (flat-wounds, ground-wounds, etc) in a tighter cone than others. They also have a bit more tension at 440 than round-wound strings and can actually lay closer to the neck than round wound string; lowering the action without buzz.
A screwed up fret can also make for a considerable fret buzz if one fret is quite a bit LOWER than the rest of them! A tweaked neck can obviously cause fret buzz also.
Obviously this is the first place to start.....
Take the guitar and bring the bridge saddles up a bit until you have no buzz. Then sight down the neck from the bridge side. IF you have a deep curve downward (a valley) you may need to tighten that neck up a bit. IF you bring the bridge saddles up as high as possible and you still get buzz; look at the neck, if you have a bow upward - like a hill; you need to loosen the neck.If your neck looks straight, the strings are fairly high and you STILL have buzz, take a GOOD quality ruler (a quality straight edge!) and check your frets for consistent height in relationship to neck relief.
However if you have all in order with your setup, remember that you can't rip into any string like an archery bow and expect it not to buzz. Check your technique if all else fails. Good technique is placing your finger RIGHT BEHIND THE FRET - NOT in the middle, pressing down hard into the fret wire just behind it with the pad of the finger plucking the string with light to moderate force in a parallel line with the pickup surface, etc, etc. Use as basic a technique as humanly possible to determine if some issue exists with pickup height as well!
Remember you have 4 factors you can work with right off....
Good luck!