Shrunk rides are for secure storage and trading. Pets are shrunk through the use of Shrink potions which are made by GM Alchemists from 15 dead wood reagents (fail rate is ~50%). If you happen to find someone selling Shrink potions, expect the price to be ~3-4k. Obviously, leave shrinking for valuable pets.
Prices for rides tend to be as follows:
Remember that an animal "remembers" all his owners since the last taming, hence if you're paranoid about someone getting their hands on your bought ride you'll have to release and re-tame it. Then sometimes Shrink potion won't work on your pet, claiming it's not yours. Again, you'll have to re-tame it or transfer it to somebody you trust for shrinking. Although just trasfering it to yourself will work too.
If there is nobody around except for your 1 pet, it's ok to give bare commands. Otherwise you'll have to precede the command by pet's name or "all" if the command allows it. Commands that doesn't support "all" keyword will apply only to 1 pet. Usually it's the last tamed/summoned pet.
To tame you'll need a Taming Stone. Dispencers are in Runestone Chamber and near Wind bank in the form of a Brown Bear statue. Keep your pets fed or they'll go wild shortly after starving. It's sorta inconvenient having your ride drop you off in the middle of the fight.
You can buy Pet Protection Potion from some NPC Alchemists to protect your pet upon death. Supposedly it should teleport the animal to the spot where the PPP was used on it. It also makes the pet blue, which might discourage some players from attacking it, but the repercusions are like nothing to be concerned about. You won't be able to use ppp if your pet is already blue from karma though. Also, it sometimes gets confused as to who owns it and wouldn't let you ppp it, like with shrink pots. Transfering for someone else to do it will work fine.
However the script is off and your pet will almost never poof to the desired location. With the non rideable ones it might work for the first time, but after that it's pretty much random and not in your favor. Mounts usually will poof to tutorial area and staff seem to be giving them back. So it's still nice practice to use ppp.
Mounts seem to lose their poofing location when you get on them. Their home var gets reset or smth. If you don't get on them however, and had "all come", "all follow" or "all guard" said to them before death, they'll poof to their correct location of ppp used most of the time. If they had been told "all stay" before death, they'll poof to the spot they're standing in, i.e., won't move. The shrinking/unshrinking and then use of ppp has been told to help with ride poofing to the correct location, but it's pricey and still seems to be random.
And avoid buying pets with PPP already used on them if you intend to use PPP yourself, as it's effect is long lasting (if only single - need to use it again after pet's "death") and animal will retain it after going wild, retamed or shrunk.
Be carefull not to use PPP if you intend to shrink it. As part of an attempt to fix ride poofing you can't shrink PPP'ed animals atm.