Alternate nostril breathing does what the name says it does. You close one nostril, breathe in, then close that side and breathe out through the other, going back and forth. The right hand usually does the work, thumb on one side and ring finger on the other, though any grip that lets your hand rest without strain will serve.
Classical texts like the Hatha Yoga Pradipika describe the body as run through with nadi, the channels that carry prana. This practice cleans them out, which is where shodhana comes in. Evening out the flow between the two sides tends to feel like settling. Less scattered, more ready for whatever comes next.
Many traditions teach a ratio of inhalation time to exhalation time, so many counts in and so many counts out. In Kripalu Yoga we leave out the counting, since it can bring tension into the body. Relax into the pranayama instead and let a ratio develop on its own. As the in-breath and the out-breath flow at their own pace, the breath slows down without anyone pushing it.