I know that a sailor can sail and steer without rudders using the sails to influence direction. Can you guys give us the skinny on this?

Mainsail out...boat heads up.

and/or

Jib in...boat falls off.

Your weight placement will affect this as well, generally moving weight to the side of boat whose direction you wish to go works as well (with sheet/sail in stationary position)

Actually, it works the other way. Main in, boat heads up.

That's right.

The sail plan has a Center of Effort (CE) that moves fore and aft, depending on sail trim. More pressure on the jib, it moves forward. More pressure on the main, it moves aft.

Likewise, the hulls have a Center of Lateral Resistance (CLR). Bow down, it moves forward; bows up, it moves aft.

If the CE is forward of the CLR, the boat will head off (lee helm).

If the CE is aft of the CLR, the boat will head up (weather helm)

The distance between the CE and CLR determines the strength of the helm. More distance - more helm.