How should I position a motion sensor?
IR motion sensors can be thought of as a low quality camera with only one color, IR. They are constantly comparing the IR levels across a grid to see when there is a quick change in IR levels. When you look at the housing of a sensor, you can see this grid, and unlike that of a digital camera with mega-pixels, these sensors only have a dozen or so measurement points.

Motion directly towards or away from a sensor will show only a small change in IR at the same point. Therefore, you typically want the sensor position to detect motion from side to side. Locate them in places you need higher levels of security, like your home office, or in places a burglar would have to pass, like a stairway or central hallway. You also want them positioned that a pet could not accidentally trigger it, either by aiming high or by placing them in parts of the home that would be closed off.

Also, since these sensors are detecting a change in heat, avoid pointing them towards HVAC vents or other sources of quick temperature change. And avoid pointing them towards windows since IR can pass through glass (though various coating on newer windows should reduce this problem).