For this example, let's assume /dev/sda is the good/working member, and /dev/sdb is the failed (or newly inserted) drive:
1. "cat /proc/mdstat" to verify the condition of the array (which "md" members are present, which drives are good/missing/etc. for sanity):
2. Mirror the partition table from /dev/sda over to /dev/sdb using the following command:
ELSE
3. The new drive should now have a matching partition scheme to the existing (fdisk -l can validate). Re-integrate any of the RAID1 partitions back into the array (using the information from "cat /proc/mdstat" to match the partitions the the md members):
4. Apply the boot-loader to the Master Boot Record of the new drive, to ensure the new RAID members work on boot, using:
5. The current rebuild status should be visible with: "cat /proc/mdstat", assuming nothing went wrong with the above, you should be done, and the RAID should finish rebuilding on its own from here on out.