Q3 and Q6 supply an amplified signal to the H bridge.
This signal (+ or -) is taken to the bases of Q1 and Q2 which are joined together. Thus if a + signal goes to a pnp (Q2) it turns it on, while simultaneously turning off the npn (Q1).
Thus either Q1 or Q2 are turned on at any given time, but not both.
Suppose a + voltage comes to the bases of Q1 and Q2, Q1 turns on, and Q2 off. This supplies current to the motor from left to right.
The exact same logic applies to Q4 and Q5. Suppose a negative (0V) voltage is applied to their bases, Q5 turns on, but Q4 turns off.
Thus current flows from the top (+ power supply), through Q1, through the motor, to Q5 and ground. Reversing the bases causes current to flow from the + supply, through Q4, through the motor, through Q2 to ground, reversing the motor.
The diodes and resistors are there to protect, so ignore them for now.