Adruino External Pull Up Resistor Confusion
You need to connect the Output from the sensor to pin 10 of the processor board then also connect one end the resistor to the same pin 10.

The other end of the resistor should connect to +5V(VCC), such as pin 4.

It is called a pull-up because it pulls the signal pin up to 5v when the source isn't driving it low.

Some types of signal sources only work in one direction.  In this case the sensor can force the signal to ground but does nothing in the other state.  It relies upon the pull-up to set the signal level - hence the need for the pull-up resistor.