WIth the replacement drive in the unit, power the unit up by flipping the power switch to "on" and wait for the unit to boot.
You will be getting error codes at this point, because the NAS still sees the disk as a problem until the array is rebuilt.
Log into the web admin page for the unit by typing its IP address into your web browser. Login with admin and your admin password ("password" by default).
In the menu: System > Storage
Under RAID Array you should see "array 1", which is a link. Click on this link, and you see see the option to rebuild the array.
If you do not see this option, or it is grayed out, highlight the new disk under "Disks" and select Rediscover. After the disk is rediscovered, click on array 1 again and you should see the option to rebuild the array. (you may have to select Remove before selecting Rediscover).
You will get a message telling you that the disk used for rebuilding the array will be formatted - this is talking about the new disk, not the one with your information on it. Continue through this message, enter in the displayed confirmation code, and that's all.
You will not be able to access the data or make any changes in the interface for a few minutes while the array is configured. After this, you will have normal access to the drive, though still with degraded performance until the resyncing of the array completes.
The resyncing takes 4-5 hours per TB TOTAL CAPACITY. Until the resyncing is complete, you will see an info/error code flashing on the unit, and it will be noticeably slower to access. I recommend not using the NAS until the process is complete, as transferring data will just make the process take longer.