I'm not saying this will completely rule out any possibility that something is up with the brake booster, but to check that it's functioning correctly (at least at the moment of the test) here are the steps:

First thing is you press the brake pedal several times (w/ engine off) to build pressure and then while holding your foot hard on the pedal, start the engine. The pedal should sink slightly, if it doesn't sink at all it would indicate a problem with the booster itself or it's check valve.

To test the booster for leaks: Press on the brake pedal while the engine is running (not sure if it matters that it's at normal, warm idle) and then turn off the engine while continuing to press on the pedal. The pedal height shouldn't vary, if the pedal starts to rise it would indicate a faulty booster.

To check that the booster check valve is working, press the brake pedal several times with normal pressure while the engine is off. It should start off low and gradually rise as you keep pressing it over and over again. If the pedal height doesn't change, you should check the booster check valve directly.

To do that, disconnect the booster vacuum hose where it attaches to the booster itself. Start the engine and let it idle, you should be able to feel vacuum. If not, the check valve isn't working.