If you want simultaneous access to the diskgroup/volumes/filesystems, you need CVM/SFCFS - this requires additional license. Check vxlicrep -e output to see if the feature is enabled - if not, you'll need to speak to your account team to obtain the extra license, then install the additional product components.
Note: if you're planning on using Oracle concurrently you will need SFRAC which is a different product/has more features (and you'd also need to purchase Oracle RAC license from Oracle).
If you do plan to use SFCFS, would strongly recommend you take a look at the Installation and Administrator's Guides (SF 5.1 for AIX versions below)
Veritas Storage Foundation Cluster File System Installation Guide
http://sfdoccentral.symantec.com/sf/5.1/aix/pdf/sfcfs_install.pdf
Veritas Storage Foundation Cluster File System Administrator's Guide
http://sfdoccentral.symantec.com/sf/5.1/aix/pdf/sfcfs_admin.pdf
this may also be helpful:
Veritas Storage Foundation: Storage and Availability Management for Oracle Databases
http://sfdoccentral.symantec.com/sf/5.1/aix/pdf/sf_adv_ora.pdf
Further documentation is available here: https://vos.symantec.com/documents
If you just want to know how VCS handles failover diskgroups (for private/non-shared diskgroups) - see the VCS User's Guide and VCS Bundled Agents Reference Guide for details
VCS Administrator's Guide
http://sfdoccentral.symantec.com/sf/5.1/aix/pdf/vcs_admin.pdf
VCS Bundled Agents Reference Guide (see: Storage agents -> DiskGroup agent)
http://sfdoccentral.symantec.com/sf/5.1/aix/pdf/vcs_bundled_agents.pdf