While I'd love to do more sessions than I currently do (work ebbs and flows from year to year, but I still stay busy) - I'd say:
-Relationships
-Location
-Attitude
-Aptitude
Pretty much in that order!
You need a pool/community of other session-quality musicians that you are friends with and can work with for long hours, sometimes for lousy pay and often on music that drives you nuts!
You need to be somewhere with lots of studios and people recording music. Obviously! While 'remote' sessions (recording at home and file sharing) have increased, it seems to have plateaued. Location used to mean NY, LA or Nashville, this is less true now, but more studios means more work!
You need to have a positive vibe and presence that makes others want to be around you and even helps them play better.
You need to be able to play. A little technique, great tone, quick instincts, taste, good ears, gear that you know and works well - it's all a given prerequisite & takes time to develop!
All that & a spouse with health insurance & you're good to go! ;-)