Strength training can compliment and be informed by a yoga practice.
Weight lifting can help overcome asana obstacles, especially for arm balance and power oriented postures.
If you find yourself struggling with a particular asana or a particular type of asana (arm balance, deep lunges, etc), ask your teacher if s/he notices a weakness in your practice. Perhaps you need to work on your core or your upper body strength. Maybe your lower back or quads need extra attention.
Incorporate strength training in to your health routine and give extra attention to the areas of your body that are holding you back.
Weight Lifting: I recommend doing 18-22 repetitions with a lighter weight for the first 2-6 weeks of any new strength training exercise. Increase the weight you are using gradually over time (every 3-6 workouts), and maintain high repetitions. The goal is to max out (or become too fatigued to do another repetition) by the 20th rep. I am a strong proponent of only increasing weight by 2.5-5 pounds and waiting until the current weight choice is clearly manageable before increasing your weight.
Asana Practice: Chaturanga Dandasana is a difficult pose for many people. The transition from Chaturanga into Upward Dog, can be even more precarious if core or upper body strength needs improvement. A proper Chaturanga looks like this:
If this pose or the transition to Upward Dog is difficult for you, come down on your knees and do Chaturanga push-ups.
Multiple repetitions of the same action increases strength. If you can’t hold a pose properly, you may be injuring yourself. Make a difficult pose easier by taking a modification, then hold the pose longer or do a transition over and over. You will reach the peak pose quicker and with more integrity.
Lesson Learned: Hit the gym 2-3 times a week in order to strengthen parts of your body that are holding your asana practice back.