I'm acting as a consultant for an ICT company and we are pretty familiar with IT, from HW through SW including Networking. Just to make the conversation easier and to give you a feeling of my (our) knowledge level, just to avoid basic things. When the rebuilding is about to begin, it should warn you about erasing the data from the new disk just ignore it, there is no data on the new disk (but they assume it might be). The data is mirrored on the other disk, so you will not lose any of it. The NAS should have an IP address that you can punch in your browser and should take you to the management window, kinda like setting up a router. Need to go into the NAS management (usually a browser-based window) and tell it to rebuild it from there. Remove the bad HDD and insert the new one, same capacity or greater.
If you know how to open up the enclosure, it should be pretty straightforward.