And so you might ask. Why choose binary or multiple stars for an observing programme? There are several reasons to observe these objects, not least of which:
There are many resources available to help you learn about these stellar gems, including books, catalogs and websites. I began with "Observing and Measuring Visual Double Stars" edited by Bob Argyle. It is a somewhat technical book, but full of very useful information for the curious amateur, and throughout it has a very positive attitude. There is a new book from Sky Publishing entitled "Double Stars for Small Telescopes: More than 2,100 Stellar Gems for Backyard Observers" by Sissy Haas, but my copy has not arrived yet.
Measuring binaries is a matter of determining the separation of the components in arcseconds, and determining the angle between the primary and secondary with respect to the celestial north. It sounds easy, but getting sub-arcsecond precision is a tricky business. A variety of methods are available, including optical micrometers, diffraction gratings, drift timing, and digital imaging. With any of these, calibration is always an issue - if the calibration is off by even a fraction, the measurements will be useless. The classic method of binary measurement is to use a filar (or bifilar) micrometer, which can measure the separation and angle directly, and by taking multiple samples, and average can be obtained. But these instruments are out of the price range of the Budget Astronomer. Being cheap, I created my own method, combining drift measurement and image analysis of webcam images. The resulting software, called BinStar, is available here.
My colleague Florent Losse in France also has a (rather more sophisticated) piece of software called Reduc for mesuring binaries using FITS files, which can be produced by a webcam using software such as K3CCD tools.
If you decide to pursue binary observing, and you decide to use a camera for the purpose, I would highly recommend you invest in a flip mirror, which enables you to locate and centre the target visually, and then flip the mirror out of the way to enable the camera to "see" the target. Trust me, with the tiny chip size of most webcams it will make your life a whole lot easier!