regnak: Is there a trick with using the lance?
What you want to do is “couch” the lance – have your character lower it into a horizontal position at their elbow and keep it there, then steer the horse so that the lance’s tip will collide with the target. The exact process for doing this depends on whether lance couching is set to manual or automatic in the game’s settings. Also, to do this you will need a weapon that's actually classified as a lance by the game, not the wooden staff you start with in the training area. The horseriding trainer will spawn a practice lance after you complete his first task (riding to a bunch of checkpoints).
If lance couching is set to manual: mount your horse, equip the lance – in the bottom right corner of the UI, next to the lance icon, you will see a small dot. When that dot is red, the lance cannot be couched (you either don’t have enough speed on horseback or the couching is on cooldown after use). When it’s white, the lance is “cauchable”. When the dot is white and you want to couch the lance, press the alternative attack key (default: x). Your character will couch the lance for a few seconds.
If lance couching is automatic and you have a lance actively equipped, once you gain enough speed on horseback your character will lower the lance to their side automatically. After some time they will raise it (cooldown period) and then lower it again, as long as you maintain the required speed.
To hit your target effectively, ride towards it with your lance couched, steer your horse and adjust your character’s position in the saddle so that the only the lance’s tip will make contact with the target (the horse should ride past the target either to the left or right, not into it).
regnak: Then with the horse archery I see the jerks riding by who keep turning in their saddle to fire. How do I do that?
With an equipped bow and arrows click the attack mouse button to start drawing your bow. While the targeting reticule is on screen, you can rotate the character in the saddle using your mouse pointer (the direction keys still control your horse’s riding direction).
Note: you can click and hold the mouse button to draw and hold the arrow on the string for a longer while, giving you more time to aim. Initially this will also improve your aim (make the targeting area smaller) and the damage dealt (more strength put into firing the bow). However, as you continue to hold the arrow on the string, both your aim and damage dealt will get worse (reflecting your arm being tired). Also note that your character can only fire at a certain angle – beyond that angle the targeting reticule will disappear and the shot will be ineffective.