You can take out the failed disk and replace it with a new disk while the ReadyNAS is online (there's no need to shutdown the ReadyNAS). Make sure after taking out the failed disk, you wait about 10 secs before inserting the replacement.
On older ReadyNAS systems (ReadyNAS 600), you'll need to shutdown the ReadyNAS and replace the failed disk while powered off, and then power-on the ReadyNAS. Once the replacement disk is in-place, the disk will be initialized and sync'd into the RAID volume.