First off you need to make sure that your Command / Branch has webmail enabled. The Navy and Air Force have it so I would assume the Army does. Once you know the web address and default server location you can access it was a CAC.
Army CIO/G6 Blog titled: Army Nears Completion of Migration to Defense Enterprise Email (hear what others are saying about EEmail. All Army AKO users who have a CAC should now be migrated to DISA's Enterprise Email and will no longer be able to access email via username / password.