Repairing a degraded raid mirror. Assuming sdb1 has fallen out of the mirror:

Check to see if the disk thinks it should be in the array

mdadm -E /dev/md0
mdadm -E /dev/sdb1
mdadm -E /dev/sda1

Readd the missing disk

mdadm /dev/md0 -a /dev/sdb1

Check to see the array is rebuilding

mdadm -D /dev/md0