What steps we need to perform from DB end in case of storage migration?
The impact should be minimal, if not non-existent. I've had several databases of varying sizes (both in storage and cluster) and types (MySQL, Postgres, Cassandra, to name a few) migrated between different storage environments with little impact to the end user. The VM always stays online and is usable just as it was prior to the vMotion.
If it's a:

manually triggered event I would say, at minimum, have a fresh backup available somewhere off-server in case there is a problem that requires a recovery. Otherwise, watch your applications and logs on the DB server as the Storage vMotion is occurring  and react accordingly.
automatic event because of storage failure, storage utilization, etc., you should be sure your backups are automated and saved off-server so you can recover should there be a problem. VM snapshots won't save you here should there be a problem.