If you have ever been to a yoga class or seen yogis practice online, you must know that they are beasts. Yogis are strong. Going from adho mukha vrksasna (handstand) into kudinyasana (arm balance) requires an immense amount of strength. Forget about these advance arm balances for a second, even to do a chaturanga you have to be fairly strong.
First off, any posture/ asana in yoga requires well developed abodminal muscles (iliopsoas, rectus abdominus etc.) Your abs are the center of your body, hence the main location for stability and enabling balances of all kinds. The most basic exercise to strengthen these muscles is the plank. If you have lower back problems, the plank pose puts little strain on the lumbar spine. Start out by holding a thirty second plank. Once you feel as if you are getting strong, keep adding thirty seconds until you get to five minutes. Once you reach five minutes call me, so I can congratulate you and stare at you enviously in person. If you've tried plank and like me, if you get bored after twenty seconds let alone two minutes, then do a straight arm plank for thirty seconds and switch to a forearm plank for thirty seconds. Keep repeating this sequence until you've reached your time goal. Another excellent abdominal exercise, is navasana/ boat pose. Hold navasana for two breaths, then lower half way down to a hollow body hold. After holding the hollow body pose contract your core and come back up to navasana. Repeat this ten times. Keep adding more sets as you get stronger.
The other major muscle that is used fairly frequently in yoga is the triceps brachi. Most poses including chaturanga dandasana require a well developed tricep muscle. There are many exercises that could preform this task. One of them is just repeating the chaturanga series with added tricep pushups. Come to a downward facing dog, I mean now, stop reading this and try it, roll your hips like a wave into plank, hold here with your heels pressing towards the back of the room for an inhale, on the exhale, lower halfway down (KEEP YOUR BELLY OFF THE FLOOR AND ELBOWS SQUEEZED IN SO TIGHT THERE SHOULD'T BE A GAP) then raise back up to a planck then lower again, un-tuck the toes and pull your chest through to an upward facing dog (DROP THOSE SHOULDERS AND NO SICKLE FEET), come up to a downward facing dog, adho mukha savasana (gotta learn sanskrit). Repeat this, but now do three triceps push ups before coming to an upward facing dog, ardha mukha savasana. Keep doing this sequence until you get to ten. Once your triceps, say man I've had enough, don't stop, drop your knees. MAKE SURE YOU GET TO TEN, unless you break a bone then stop. Other tricep exercises include adding weights, either in the form of dumbbells, the tricep rope, or using your body as a weight such as doing a chin up or using a TRX.
I hope these basic exercises will not only improve your yoga practice, but also make you feel stronger and more like a badass, in a peaceful yogi way. If you want to share any other exercises, feel free in the comment box.