Can't get the archer to fire on the attack, only responds on defensive. HOW do I get the archer to attack.

P.S. The archer fires fine on defense. On the attack it doesn't matter if I've moved or not.

That depends on what you want to attack. Archers don’t have range, so to attack another ground unit you would have to move it right next to that unit (and hopefully you have a melee unit that move in front of the archer in the same turn so that the archer never is exposed to an enemy counterattack as archers are quickly killed by cavalry).

If you want to attack a flying unit the archer has to be right under that unit.

You attack with archers the same way you attack with any unit. The only difference is the unit you're attacking doesn't get a counter-attack like it would if you attacked it with infantry or cavalry. As Conjurer Dragon said, archers can also attack fliers, but only if they're in the same hex.

You don't usually want to use archers to attack though. They shouldn't be on the front line, but a row behind it since they cover all adjacent friendly units with defensive fire. In other words, if an enemy cavalry unit attacks one of your infantry units, and you have an archer unit next to the infantry unit, the cavalry unit will be counter-attacked by both the infantry unit and the archer unit.