Over the years I have seen quite a few runners find their way into the yoga studio. Typically the reason cited is “I'm so tight!”. Stretching muscles tight places is a benefit a runner can certainly get from yoga. I do think there are some others as well. I also think it is useful to think about what kind of practice, and what sort of asana work might best serve the runner's needs.
There are two ways to take this post: you can decide to stretch by using some asanas from yoga. This is not exactly the same as yoga, as yoga is not just asana. Or, you can do a yoga practice that includes the breathwork, focus, sequencing, balance, meditation, etc, as well as the asanas, but include emphasis on the things that help balance the work of running. Either one is fine. I of course, come from yoga and embrace the discipline fully. But I use Pilates, and weights, and other things within my work, taking the pieces that best serve my needs.
Running is an activity with repetitive movement. A three part movement is repeating over and over: pushoff, recovery, and landing. The primary muscles involved are: at the hip the flexors and hyperextensors, at the foot the plantarflexors and dorsiflexors, and at the knee the flexors and extensors. If one is going up hill the knees and the seat (glutes) will get a bit more use. So the muscles that get used most will be: the four muscles of the quadricep group, the three muscles of the hamstrings, the gluteals, in the hip iliacus and the psoas, and the gastrocnemius and soleus in the calf. There can also be some strain on the tibialis anterior (front of the shin). The hip rotator muscles are also used to stabalize the hips.
Runners actually use stabalization muscles a lot. If the abdomen is really loose and can't stabalize the low back, it is more likely that the pelvis will tilt and there will be low back stress.... and compressing the low back and then putting repeated stress on it as you land on the feet over and over is not conducive to good back health. Running with crouched posture due to weak back muscles creates stress and fatigue, and makes it hard to breathe deeply.... something rather useful when engaging in an aerobic (with oxygen) activity.
My basic practice with a tight area is to stretch everything around it, but to give extra time and attention to the tight part. This is a good way to rebuild balance, rather than to create a new tight area. So the first thing I suggest is to do stretching and strengthening activities, including all major muscles and the core along with the running. It is also really useful to speak to your health care provider if you have a specific physical limitation or injury before starting either running or yoga. For example, forward bends are really good for runners, but with certain kinds of back issues they can make things worse (e.g in spondylosisthesis it is usually better to keep the knees bent).
I also would recommend that stretching before running is probably less useful, than stretching afterward, or better yet, making flexibility a standard part of your weekly schedule, rather than just a quick tug on the leg after a run.
If you have done a lot of yoga in the past you may not need a teacher, and may have a 'home practice'. If you are new to it, there are lots of books and youtube videos, and DVDs, but working with an experienced teacher at first will give you an awful lot of good feedback and help. If it is at all possible I do recommend trying to find such a class. I have a blog post about finding a yoga teacher if you are interested.
When doing yoga try to find a teacher who is conversant with the practice of pranayama. The breath work will help your focus and rhythm. This does not mean someone who says “deep breath” over and over, but someone who will help you to understand how to focus on the breath, and the ways that the mind, the lungs, the muscles of respiration, and the working muscles function together, and how you can use that system most effectively. You also want to learn to use mulha bandha. Developing the belly strength and core control to protect the low back will help with form and flow, and help protect the spine. Vinyasa can be helpful partly because it promotes range of motion around the joints. That stretch and contract process is good for creating and maintaining joints that move fluidly. It is also a great way to work on breath rhythm and control. Forward bends are very helpful. I would suggest starting with the supine or standing bends, rather than the seated ones, as they are easier on the back if you are tight in the legs. And always balance your forward bends with some back bends, unless you have a specific medical condition that limits this type of bend. Down dog is very helpful. In addition to the forward bend aspect, you get a stretch through the plantar fascia, through the achillis tendon, and straight up through the gastrocnemius, into the hip, and as a bonus, into the shoulders. A good technique is to take a few breaths with one of the legs and then the other bent, or both bent at once, and the body weight slightly pushed back to the heels. The bent knee takes the gastrocnemius out of the stretch and lets you get into the soleus. Do be very careful if you have plantar fasciitis, or any other condition. And if your heals are quite a bit off the floor put a rolled mat or blanket under them. No it is not cheating. Yes, it lets your legs relax into the stretch, rather than fighting you by tightening so they do not get overstretched. Hip openers are also really important. I like pigeon partly as it lets you stretch the tibialis anterior as well as having multiple ways to adapt it to send the stretch into different muscle groups. If you are really tight you will probably need to pad yourself well. But there are other hip openers if for some reason that is not going to work for you. Back laying postures are particularly good.
And do not forget the importance of the meditative, relaxing part of yoga. Running can be a wonderful way to destress after a hard day, or when life is challenging. But tyoga is a place of respite as well. A teacher who follows yoga philosophically will try to provide a place where kindness is the rule, where limitations just mean one needs a slightly different path, and where all who come in the spirit of kindness and non judgement are welcomed. I think we all need a place like that sometimes.