1. Practice, practice, practice. It might sound obvious, but when you're looking to deepen your understanding of a particular pose, make a point to practice.
2. Hold it. I'm not usually a fan of holding any pose for a long period of time. (I'm impatient, and I like to move!) But I've noticed that most of my little breakthroughs for a pose or a grouping of poses have come when a teacher has encouraged me to stick with it and hold a pose even when I'm uncomfortable. I'm convinced that this is when real transformation happens.
3. Breathe. Take a deep inhale to make space in your body. As you exhale deepen your pose--twist a little more, bend forward just a little more, and so on. Repeat.
4. Learn the story behind it. When I learned that Warrior I, II, and III are representations of Shiva's rage when he learned his first wife Sati had been insulted, the pose took on a new meaning for me. Whenever I become frustrated that my teacher asks me to hold Warrior for longer than I'd like, this story pops into my head and I manage to stay just a few more breaths.
5. Let go. Sometimes the best way to deepen a pose is to stop trying so darn hard! Let go of unnecessary muscle tension. Let go of expectations. Let of the need to do more, be more, or have more. Deeper poses and deeper practice will come to you in time.