If you check the in game help, it shows all pet commands. You must have a minimum level of empathy for different commands. From the top of my head, commands they can do are /pet follow (the pet follows you around walking slowly); /pet name (name) (No parenthesis, names your pet what is in the space); /mypet (works like /me only replaces it with your pets name); /pet target (targets the thing you have selected); /pet attack (attacks and claims possession of what it has targeted); /pet assist (attacks, but does not claim possession (you can attack with it) of what it has targeted); and /pet guard (I haven't tried this, but I assume it means you can guard items from a distance since your pet is there guarding it). Pets can attack pets and people.
There are also two more cool things I found. 1 is that you can talk to your pet in the NPC tab, and 2, if you are sick of your pet following you slowly, have your pet target you then use /pet attack, it will
run after you. You just have to be careful you don't get nipped.