I just got this working so needs tweaking.
Get a stone you get a lion/unicorn or a leopard
get it to level 7 by feeding it
take it to a pet trainer with the correct items like a armor/harness and it will become ridable.
you have to wear special armor to ride the mount
It has its own 10 slot storage bag
it does NOT fight !!
You can even set up you pet as a shop then go off line !!
as you can see dave set up his own shop without a pet