Stars that are too close to see as separate stars can show their binary nature via
eclipses. In this, one star moves in front of the other and blocks its light. We see
this as a drop in the brightness of the star. The basic idea is illustrated in Figures
21.8 and 21.8 of your textbook.
Transparencies of Figures
The best example of this type of star is Algol, or 
Persei.
SC1 chart with Algol. Every two days and 21 minutes Algol drops in
brightness for a period of about eight hours. The next few minima of Algol are as follows.
September 23; 6 AM, September 26; 3 AM, September 28; midnight.
Eclipsing binaries tend to have periods of a few days, down to under a couple of days.
This corresponds to the time it takes the stars to go around each other, so obviously
they are pretty close.
Artists Conception of Beta Lyrae
Image of Beta Lyrae.
Ballpark separation between the stars in eclipsing binaries are about 10 million kilometers,
or about 5 - 10 times the stellar diameters.