According to this link here there is a 30 day full refund no questions asked warranty if purchased direct from the GoPro online store (presumably plus a 12 month warranty) otherwise it has a 12 month warranty, 24 months if you are in Europe.
Since yours is a only a few days old, it might depend on what the store that you bought it from policy is, as to what happens. Some may simply replace it with a new one, some may send it away for warranty service for you or some may state that they do not handle warranty claims and that you have to contact GoPro (as per the warranty statement) for warranty service.
Contact the store beforehand to find out what their policy is. At least this will save you the trip there if they do not handle warranty claims. If they will replace the camera then ensure that you have the sales receipt, the camera obviously, as well as all the camera accessories and any packaging etc. that came with the camera, with you when you go.
As for GoPro they only state that they will fix or replace under warranty. They do not mention whether the replacement will be a new one or a refurbished one. You would have to contact them to verify what they do.