I'm assuming you're new, so I'll explain it in some detail.
TL;DR version: You get basic ones with gold. Cooler/more exotic ones with real money OR AD to Zen conversion.
You get a companion quest at level 16 and you automatically learn the mount skill at 20, but have to buy it separately.
You start with 3 rental tokens after you do the mount quest with something like a 5 hour in-game time limit before they go away.
Basic companions and mounts are acquired through each vendor respectively. You can get cooler pets and mounts through the Zen store,
which costs $$$, but you can convert Astral Diamonds you get in the game into Zen and get real money mounts that way.
You don't have to spend money to get those exotic mounts, it just takes longer to get them with converting game currency to Zen.
Hope it helped.
This post was edited by Fire_Deviant on Jun 1 2013 05:29am