What is the proper way to breathe during strength training?

Exhale during the most strenuous phase of the movement – this is often referred to as "exhale on the exertion."  Inhale during the less strenuous phase.  It is also important to inhale and exhale fully between each repetition.

However, the most important thing is simply to breathe regularly.  Most people assume that they are automatically breathing when in fact they are actually holding their breath.  Take a moment to focus on your breathing during your next strength training session and during other strenuous activities such as climbing up the stairs.  You may be surprised to find that you are actually holding your breath.