Sometimes the strings on your guitar will buzz even when you're not fretting a note. Sometimes the strings will only buzz when you do fret a note. There are ways to figure out and fix this common problem.
If your string buzzes when you simply play it open, the problem is that the string is vibrating against the metal fret somewhere on the fret board. Basically, the string is too close to the fret to vibrate freely and not come into contact with the metal fret.
The cheapest and easiest quick fix is to take all of your strings off, and put a little piece of paper underneath the saddle to raise it up a little bit. Over time either the string can eat at the plastic, causing it to be a bit lower, or the pressure from the strings can push the saddle down. This obviously causes the action to be too low. The "action" of a guitar is how far away the strings are from the fret board. This fix tough is only temporary and is not the best route.
The other fix is to get the truss rod adjusted at a music shop. The truss rod adjusts the curvature of the neck, which will directly affect the action. Do not try this yourself because you could permanently hurt the guitar. This might give you higher action, but the buzzing should be fixed. A guitar expert will know the exact curvature of your neck so that your strings will be as close to the fret board as possible without buzzing.
If your strings only buzz when you fret a note, odds are you need to press down a little bit harder on the string, or you need to move your finger closer to the middle of the fret. If you are sure that you are pressing down hard enough, then you may want to take your guitar into a shop to have them look at it.