Combat is treated just as it would should you be on foot, you would make a ride check to guide the mount as a free action and then make an attack at the end of your charge. If you are using a Lance you would double your damage at the end of the charge.
I have included a bunch of text that, for the most part, is relevant below:
With a DC 5 Ride check, you can guide your mount with your knees so as to use both hands to attack or defend yourself. This is a free action. If your mount charges, you also take the AC penalty associated with a charge. If you make an attack at the end of the charge, you receive the bonus gained from the charge. When charging on horseback, you deal double damage with a lance (see Charge).
In order to move -> attack -> move, you would need the Ride-by Attack Feat - Ride-by Attack (Combat)
Your horse's stats will apply only to your horses actions. So say you are riding a mount that can make an attack, it would apply its attack after the move action.
Horses, ponies, and riding dogs can serve readily as combat steeds. Mounts that do not possess combat training (see the Handle Animal skill) are frightened by combat. If you don't dismount, you must make a DC 20 Ride check each round as a move action to control such a mount. If you succeed, you can perform a standard action after the move action. If you fail, the move action becomes a full-round action, and you can't do anything else until your next turn.
This last bit of text is not necessarily relevant, however it was the only text I could find that mentions mounts being able to make move and standard actions in combat. Hinting at the mount being able to make a single attack.
Check the horses special abilities: (You may need to have the horse combat trained)
Docile (Ex) Unless specifically trained for combat (see the Handle Animal skill), a horse's hooves are treated as secondary attacks.
The charge would count as a full attack action so you would only get a standard action worth of attacks with the horse. (I believe this is a single hoove attack)
Because the attack is considered a charge, you can also apply combat maneuvers such as Overrun. As DoStuffZ mentioned below, there are feats such as Trample that enhances what overrun does by allowing your mount to make a hoof attack at the end. Normally you would be replacing your attack with the combat maneuver to knock them prone, in this scenario you would be knocking them prone and then receiving a +4 bonus to hit for your horse's hoof attack.