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All of the rules I can find on mounts and how they work deal with what happens when I'm riding my mount.  I assume I can move normally based on the mount's speed and makes attacks with the mount and use it's abilities.  Let's say I'm dismounted though.  Can I give it basic commands like "Attack that creature" or "move over there" sort of like a ranger's beast companion or does it just stand and defend itself until I get back on?  Can it make skill checks and follow me or use it's abilities while I'm dismounted?

Depends on the DM.

As a DM I would say it depends on the mount in question.

If you are riding a riding lizard then I would say it retreats to safe distance and waits for you. If you are riding a dragon then I would say that it gets its own turn of actions, but would make the encounter harder to compensate. 

An adventurer and his mount have separate sets of actions on turns they aren't mounted, starting on the turn after dismounting. 

RC 254 Actions (Adventurers Only): If the adventurer dismounts, the two still share one set of actions on that turn, but have separate sets of actions on subsequent turns.

How different mount react while dismounted may vary. Left to its own devices, a typical mount avoids combat, generally retreating to safety, unless it was specifically trained for battle, is defending itself, or feels unusually protective of its rider.

RC 254 Mount Attacks: The mount takes a -2 penalty to attack rolls. While not being ridden, a typical mount (such as a riding horse) rarely attacks on its own, unless it has been trained for battle, is defending itself, or feels unusually protective of its rider. Left to its own devices, a typical mount avoids combat.