Blower resistors are a common failure point on BMWs, particularly on models from the early 2000s. The first thing needed is the year and model of your car. Without that information, I can't tell you anything specific about fixing your car.
Typically, the failure pattern for a resistor is that you start to loose different fan speeds until it works only on high speed, and then stops altogether. I'm sure, however, that there are other failure patterns.
If you have a late (1996+) e36 3-series, there is a capacitor that fails in the control unit causing random behavior.
http://www.frontiernet.net/~papi/Clim_Ctrl.html
You can look up the resistor on any on-line parts vendor to see what it looks like, but when you look under the dash, all you will be able to see is the plug, because the distinctive-looking heat sink is inside the air duct.
Google your model number (e36, e46, etc) and then the phrase "blower resistor replacement". People have posted a number of UTube videos and pictorials showing how to replace resistors in various models of BMW. Even if you cannot find your particular model, you can look at some others and get a good idea of what is required.
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