How do Throttle control and Propeller control work together?
In a constant speed prop, the prop control lever basically changes the speed of the prop (it is not always running at the same speed as you indicate in your question, but rather once the speed is changed by the prop control lever, the governor keeps it at that speed). If power (or airspeed) is changed, the blade angle will automatically change in order to keep the prop turning at the same speed (within the limits that it is designed for).  

Since adding power would normally increase the speed of the prop, the governor automatically changes the blade angle in order to keep it at the same speed.  The same is true when power is reduced or airspeed is changed.

Thrust is changed by engine power because, even though the prop is turning at the same speed, the angle of attack of the prop has been changed, which changes the amount of thrust.

For more general information about how a constant speed prop works, see this question and answers:
How does a Constant Speed Propeller Work?