Only certain weapons are suitable for use while mounted.
A mounted character attacks using a modified stand and attack action/reaction, which he/she may take during his/her mount's or the target's movement actions (if that movement brings the target into his/her strike zone).
A mounted character's attack dice rolls are affected by him/her being mounted (lack of riding skill makes it harder to attack while mounted, but a mounted character gains a bonus when striking with a melee weapon due to height advantage).
A mounted character striking with a melee weapon may gain a charging bonus on his/her damage dice roll, as a result of his/her mount's speed.
Finally, when a mounted character aims a blow at a target on foot, the modifiers for aiming blows are modified as a result of his/her height advantage.