It sounds so simple when I say it out loud: every yoga pose is about angles, curves or straight lines, and sometimes a combination of all three. Here's a handy tip-sheet for what to focus on in each. Angles: Many standing poses are about angles -- right angle bend in the front knee, feet pressed down parallel or at 45 degree angles, legs straight and folding over them. Seated postures when you have your legs crossed are also about angles -- as are laying postures where you extend your legs into the air or over head. In standing "angle" poses, focus on making sure your knees and toes are aligned, and that you are lengthening through your neck.
Curves: Like the partner pose at the left (also referred to as Acro-yoga - super fun!), poses that involve curves are about stretching your side body, back bending or forward bending. Focus on breathing into the area that is exposed, and on bending/curving evenly through the entire spine. Breathe into the pose; the inhale creates space, and the exhale moves you further into it.
Lines: Yoga is all about extensional energy, and many poses involve sending your energy lines in two directions. For example, in Mountain Pose (Tadasana) you are sending your legs down into the earth, and your torso and crown up into the sky. Focus on holding strong lines, shooting laser beams out of your finger tips when your arms are extended, and rooting firmly through the feet (or the sits bones if you're on the ground).