How can I tell which volume the operating system is on?

Open Terminal.app and run df -h /:

% df -h /
Filesystem     Size   Used  Avail Capacity  Mounted on
/dev/disk1s2  111Gi   75Gi   36Gi    68%    /

On my machine my OS drive is on /dev/disk1s2. With this information you can use the Disk Utility app and find out what physical drive your OS is on:

Using diskutil from command line you're OS drive will be whatever correlates to what the df command output gave you:

% diskutil list
/dev/disk0
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *500.1 GB   disk0
   1:                        EFI                         209.7 MB   disk0s1
   2:                  Apple_HFS Nymeria                 499.2 GB   disk0s2
   3:                 Apple_Boot Recovery HD             650.0 MB   disk0s3
/dev/disk1
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        *120.0 GB   disk1
   1:                        EFI                         209.7 MB   disk1s1
-> 2:                  Apple_HFS Untitled 1              119.2 GB   disk1s2
   3:                 Apple_Boot Recovery HD             650.0 MB   disk1s3

If you're unfamiliar with how UNIX-like operating systems (OS X) partition a drive check out this Wikipedia article.

And if you want to get all the details for the root partition directly in terminal, run

diskutil info $(df / | tail -1 | cut -d' ' -f 1)