The Eight Limbs of Yoga are
Yamas - restraints
Niyamas - observances
Asanas - postures
Pranayama - breath work
Pratyahara - withdrawal of the senses
Dharana - concentration, which leads to
Dhyana - meditation, which leads to
Samadhi - Complete unity with the Self
In ashtanga vinyasa yoga, the sequence of poses is considered a complete way through the eight limbs of yoga. The first two limbs, a practitioner cultivates in his or her life while practicing the asanas. This is also cultivated through the use of intention in practice. After some time with practicing the asanas, there is a formal pranayama practice in ashtanga vinyasa yoga. The pranayama practice is introduced by a qualified teacher. From the instruction that I have received, there are a couple of techniques that are fine to introduce to students who may not be ready for the full formal pranayama practice. As for what we are doing, I can introduce these techniques in class, and complement our pranayama practice with other breathing techniques that we know and love such as the three part breath, six part breath, and alternate nostril breath.
It is advised that the yoga practitioner concentrate his or her practice in the first four limbs and subsequently, the other half of ashtanga yoga will develop naturally. If we are fully concentrating on postures, breath (this includes bandhas), and dristi (gazing point), over time we will naturally flow into a withdrawal of the senses, thus bringing about a state of concentration which leads to a meditative state which eventually brings about samadhi, the final merging or Yoga.
How long does it take? Coming to a state of meditation where the mind is at complete rest is a tricky thing. We use our brains to process this information, and so, is immediately accessible to the mind. It is easy for the mind to fool us into thinking that we have achieved things that we truly have not achieved. I think it can work the other way. Maybe we do not believe that a final unity in our lifietime is possible and so we block ourselves because we don't think that it can or has happened. This think is overseen by the mind. The best that we can do is to be clear about our intentions when we practice and be the watcher as we move through the process on and off the mat.