Orbit each other about their center of mass. Can see both stars and follow their orbits over time. Cannot separate the two stars, but see their orbit motions as Doppler shifts in their spectral lines. Here are two movies showing visual binary stars, one with a circular orbit, the other with an elliptical orbit, emphasizing the point about their orbits around their common center of mass in all cases. Solve the equation above and separate Masses.
Most binaries are too far away to be able to see both stars separately.
Here is a movie showing a spectroscopic binary star. Can't tell how the orbit is tilted on the sky Everything depends critically on knowing the distance. A JAVA-based Binary Star Orbit simulator at Cornell. Shows changes in spectral line Doppler shifts as the stars orbit, and lets you change various orbit parameters to see the difference between the true orbit in space and the projected orbit that would be observed from Earth. See a periodic drop in brightness as one star eclipses the other.