OS X installation on external HDD
The disk which you don't boot on will show as an external drive to your current OS HD. You'll have full read/write accesss, Spotlight will start indexing it.

To prevent Spotlight from indexing your second drive, open a Terminal window and type: 
    sudo mdutil -i off /Volumes/2NDDRIVENAME

and replace "2NDDRIVENAME" by the name of the disk you want to exclude. Beware if you have a space in the drive name, you may need to use the "\" escape character:

sudo mdutil -i off /Volumes/MacHD

sudo mdutil -i off /Volumes/Macintosh\ HD