Like Kat said, you might just need a little practice and the buzzing may be just a product of your developing thechnique.
However, when you release a note and there is a slight buzzing, this could be one of two (or more) things.
The first is that you may need a truss rod adjustment, and this is not something that a beginner should attempt on their own. Take it back to where you bought it and they will likely fix it up for you on the spot.
The second issue could be that the nut slots are cut too deep, or you genneraly don't have enough nut height. This will cause open strings to buzz, but fretted notes will sound O.K. There are a few quick fixes for this as well that you can have done at the store where you bought it.
Either of these issues can be attributed to changing the strings from the guage that the guitar was originally set up with, and do not necessarily indicate that there are any serious issues with the guitar that you bought.