Dirga Pranayama is called the three part breath because you are actively breathing into three parts of your abdomen. The first position is the low belly (on top of or just below the belly button), the second position is the low chest (lower half of the rib cage), and the third position is the low throat (just above the top of the sternum).
The breath is continuous, inhaled and exhaled through the nose. The inhalation starts in the first position, the low belly; then moves to the second position, the low chest; then to the third position, the low throat. The exhalation starts in the low throat, moves to the low chest, and finishes in the low belly.
Rest your hands on the individual positions to feel the breath rising and falling through each position. When you start practicing, you may want to individually isolate the movement in each position, using the hands. When you have a good feel for the breath moving in and out of each position, practice without the hands.
Eventually relax the effort of the Pranayama and breathe into the three positions gently, feeling a wave of breath move up and down the torso.