You may choose any of the following positions as long as you are comfortable with them and can keep your back straight till the end of your breathing gymnastics session.
Any straight back position works: sitting on a chair, on your heels (Vajrasana), in "half-lotus" (Ardha Padmasana), "lotus on a pillow" (Siddhasana), or "true lotus" (Padmasana). The last one is considered the best for practicing Pranayama.
Lying down on your back in a relaxed way (Shavasana) might be a good choice if you are unable to maintain a straight back position during the whole breathing session. Also it's useful for relaxation, and in case you practice to fall asleep faster.
Standing is also ok, but it somewhat decreases the training effectiveness, as more energy for maintaining a straight posture should be spent.
Before starting your training, please make sure that your clothes are not too tight, and they don't hinder your body while making a full inhaling in a position chosen.