You mean like to remotely sense people moving, as opposed to measuring linear motion of something? If you mean sensing people/animals/etc. moving, the two technologies typically used are IR and Ultrasound.
For a simple IR sensor, you need an IR fresnel lens of some kind, and an IR receiver circuit. As warm objects move around in front of the lens, that moves multiple images of the object over the IR sensor, and that change in output voltage from the IR sensor is interpreted as motion. To build your own IR-to-voltage converter circuit, you would connect a PIN potodiode (with a good IR spectral response and an IR-specific window) to an opamp in a current-to-voltage configuration. The anode of the diode goes to ground or a negative rail, and the cathode goes to the - input of the amp. The + input of the amp goes to a reference, and the output of the opamp is connected to the - input via a resistor. The IR input to the diode causes a reverse current through the PIN photodiode, which gets converted to an output voltage via the feedback resistor. See figure 14.5 in Horowitz and Hill if you have that electronics book, for example.
For the Ultrasound version, you would probably use Doppler changes in return pings, I would guess, for the simplest versions. Those would miss straight side-to-side motion, though, so a better version would do some processing on the return pings to look for any multipath changes in the return echo waveform. Look for an electronics kit that has an Ultrasonic transducer on it to start your experimenting.
Here's a link to HowStuffWorks.com & IR sensor info to get you started:
http://home.howstuffworks.com/question238.htm