Replace one disk at a time with a larger disk, letting it finish initializing and syncing after each replacement (this process can take several hours depending on disk capacity, but you can continue access to the ReadyNAS), and after the last disk has been replaced, reboot the ReadyNAS. The expansion will occur at boot time. The expansion time will depend on your existing volume size, the ending volume size, and the number of files in your volume. Typically, it'll take anywhere from an hour to several hours. You will be notified by email at each step of the process.
Keep in mind that when your replace your disks, with ReadyNAS that supports drive hot-swapping, you do not need to shutdown the box before replacing the disks. Simply pull out the disk, wait at least 10 secs, and then add the replacement disk.