How do you go about learning and mastering new instruments or techniques to expand your versatility as a session musician?

When tacking a new instrument the first thing I do is try to get its tuning ingrained in my mind then learn its interval spacing/relationships between the strings. Then I learn how to play some basic progressions on them and a few scales I can improvise with if needed. 

Then take the deep dive listening to the masters of that particular instrument so I can pick up on some nuance that I might not naturally gravitate towards on my own exploration of the instrument. 

I like to play different instrument in studio session or live gigs.

it gives me different views about my musical feelings and i think that everyone should play different instruments

I've chosen to focus myself only on my main instrument (cello), but I often add new skills to my cello playing. These often show up in the form of projects I am confronted with that ask for me to try out new skills, and for those I then spend some time researching that skill by watching videos or consulting with other colleagues who are already great at those skills, to get their tips. Then - practice, practice, practice! As an artist and cellist I also am excited to learn more about my instrument and I get inspired by watching other cellists and musicians and trying their ideas out. Sometimes I attend workshops on new skill topics that I have little or no experience with, simply to expand my horizons. This helps me be a versatile session musician and for me personally is something I love to do - new skills and new musical directions are fascinating and fun to learn!