After you add in the new drive, it would be prudent to write Zeroes to every block to ensure data integrity. Those options are on the Security Options Button in the Erase tab in Disk Utility. This can be done in the background in your working System. It takes several hours as it is, More passes is not better.
Then you need to Add the initialized drive to the running RAID set. Once it shows up as a Spare, you will be offered the option to "bring it up to date" in the background. This may take all day, but your Mac is still useable while it is doing this.
The warnings at every step are un-necessarily dire. But if you cannot afford to lose data if something goes wrong, you SHOULD make a backup before proceeding.