How do chemists know what molecules they have in their substance?

Do they use an electron microscope or some other expensive equipment? Like how do they know what they have synthesized? Furthermore, how do they know what atoms are in the molecule they're observing? Does this require any math? Much thanks to all! I would like to know so I can test the potency of a substance and know that I have synthesized the correct product. And just know what chemicals are in whatever. That is if it's affordable.