The most basic way the armbar is usually taught is from mount with the opponent flat on their back. When the opp. pushes up with both hands, place your hands on their chest with one hand in front of their arms (this dictates which way you will spin) and the other behind their arms. When you push down on their chest, you spin toward the hand that is in front of the opp. arm and back into the armbar. Make sure you grab their pants or control their thumb to limit escape options. You don't need to push off on their hip when you spin. If you can get the arm/tricep (as Kibuninc suggested) and lift their shoulder, you should be able to get your butt closer to the opp.'s body for a tighter armbar.

Most people have "tells", whether its poker or fighting. Be concious of these and use them to your advantage.