The main functionality is pretty simple. If you try to mount a jousting vehicle and you do not have a Lance equipped, WoW displays an error message: "You must have a lance equipped." Joust Do It! responds to this error message by equipping a lance from your inventory, or alerting you to head to a Lance Rack if you do not have one.

So basically, if you spam right click on the intended vehicle for just a few seconds (not long at all, trust me), a lance will automatically be equipped and you will get into the vehicle.

Once you leave the vehicle for any reason (i.e. manually, end of ToC Jousting fight) your last weapon will be equipped automatically as soon as your feet hit the ground.