Click on Setup from the drop down menu in the top right hand corner of the screen.

Type "User Interface" in the Quick Search box on the left hand side and choose User Interface.

Make sure that "Enable Collapsible Sidebar" and "Show Custom Sidebar Components on All Pages" are both checked.

Navigate to Setup -> Cases -> Page Layout and Edit the detailed view of the Case Feed Layout

Click on Custom Console Components

Select the side bar where you wish to add the Gainsight custom VisualForce page along with the existing components in the side bar.  In this example we made changes to the right side bar.  Then click on Save.  Lastly save the entire Case Feed Layout.

The selected VisualForce page from Gainsight appears in the side bar along with the other existing tabs.