Since we have horses, I figured I'd combine a few pages from the SRD. A couple things below are marked with asterisks- this is how I interpret them, but see your Zem for details.

Zem made a post on this with rules that don't have existing stuff plugged into them. For his post, see here:
viewtopic.php?f=16&t=339



Start of turn:
You need a hand to guide your horse, unless you pass a DC 5 Ride check. Ride is a Dex skill. If you don't need to roll (your net modifier is +4 or better), then don't- a 1 doesn't autofail. If you fail this check, you have to choose between guiding your horse with a hand, (and thus releasing whatever is in that hand), or not being able to control your horse that round. Presumably you can't move, or the horse does whatever it wants.*

Melee Attack:
If your mount moves more than five feet, you can't take a full attack. If it five foot steps or does not move, you can full attack normally.
If your mount charges, it moves up to double its speed (100 feet for a heavy warhorse, 120 feet for a light warhorse) in a straight line, and both you and the mount gain +2 to attack and -2 to AC until the start of your next turn.
If you are attacking a creature smaller than your mount (so, Medium, Small, Fine, etc), you get a +1 to hit.
When you are ready to attack, decide who is attacking- you, or the mount. If you pass a DC 10 Ride check, the other can also attack. **

Ranged Attack:
If the mount is stationary or moves up to its speed, you can full attack before or after the move.
If the mount takes a double move, you can full attack in the middle of that move, and all attacks take a -4.
If the mount takes a run (quadruple move), you can full attack in the middle of that run, and all attacks take a -8.
If the mount takes a single move or is stationary, it can take a melee attack before or after, if the rider makes a DC 10 Ride check.

Spell Casting:
If the mount is stationary or takes a single move, you can cast before or after the move as normal.
If the mount takes a double move, you can cast in the middle of that move, with a DC 10 + Spell Level Concentration Check.
If the mount takes a run (quadruple move), you can cast in the middle of that move, with a DC 15 + Spell Level Concentration Check.
If the mount takes a single move or is stationary, it can take a melee attack before or after, if the rider makes a DC 10 Ride check. ****


Heavy horse full attack:
Hoof +6, 1d6+4 (B) ***
Hoof +6, 1d6+4 (B)
Bite +1, 1d4+2 (B/P/S)

Heavy horse single attack: choose one of the above only.
Buffing: A horse with +4 to Strength will get +2 to hit with all the attacks, +4 to damage on hoof attacks, but only +2 to damage with the bite attacks- the bite gains only half the strength bonus.


Mount falls in battle:
Make a DC 15 ride check or fall and take 1d6 falling damage. This is a use of the "soft fall" function of the Ride feat.

You go unconscious in battle:
You have a 50% chance to stay in a normal saddle, or a 75% chance to stay in a military saddle. If you fail the check, you take 1d6 falling damage.



Ride check actions:

Spur Mount: Use a move action and a DC 15 Ride check. On success, the mount gains an additional 10 feet of movement (so a heavy warhorse will have a move of 60, and a light warhorse will have a move of 70). This deals 1 point of damage to the mount if it wasn't used in the previous round. In general, it deals 2^N points of damage to the mount, where N is the number of previous consecutive rounds it was used. *****

Cover: (Zem houserule)
As an immediate action you may choose an adjacent square and attempt to drop onto that side of the horse. Made a DC 20 Ride check. Success means you get +4 cover bonus through the mount's spaces. If you fail the ride check by 5 or more, make a DC 15 Dex check or fall of the horse (you are prone on the ground).

You may return to your saddle on your turn. Make a DC 15 Ride check. If you succeed, it is a free action. If you fail, it requires a Move action.

If the horse is galloping/running ******, take a -4 to the Ride check



* It's not clear what happens when you can't guide a mount with your knees, except that you require a hand to make the mount work. My assumption is if you were holding two Orbs Of Dropping Them Kills All Things, you would probably not choose to drop one. The rules say that "without you to guide it, your mount avoids combat".
** The "Fight with warhorse" option under Ride allows you to make your mount attack with DC 10. The entry for horses allows a horse to attack, and then with a Ride check (DC unspecified), you can also attack. I'm pretty sure that means that either one can attack for sure, and then a DC 10 Ride check allows the other to do so.
*** Bite is Bludgeoning, Piercing, and Slashing- whatever is most advantageous. Hoof is at least Bludgeoning, but isn't actually defined if it counts as the others.
**** This is an assumption based on the other rules. If Zem rules that spellcasting doesn't allow you to also give the mount an attack command, then this doesn't work.
***** If you could get on a great wyrm red dragon somehow, you could, by rules, begin dealing exponential damage to it with DC 15 Ride checks. This is a great example of why you can't always just go by the rules.
****** I think this means, if the horse galloped (4x speed) on your last turn if this is happening NOT on your turn, or if is your turn and has already galloped.



This doesn't cover mounts we don't have (griffons, regular horses) and actions we don't think we need ("stay in saddle"- I don't know when the mount tries to throw you off, but there's a DC 5 Ride check to avoid that, should it do so).