It depends on the specifics of your sensor, and the specifics of your transistor. The transistor, in turn, should be chosen to support the motor you want to use.
The circuit could be as simple as a MOSFET transistor, and the sensor to transistor gate with a pull-down (or pull-up) resistor, and a big enough MOSFET for your motor -- it all depends on the sensor, and the transistor, you need.
A more generic circuit would use an opamp or comparator in between, and a potentiometer to set a reference level, and use the output of the opamp to drive the transistor.
So, pick a suitable transistor for your motor, and for whether you want top-side or bottom-side switching (P-channel or N-channel MOSFET, or PNP or NPN BJT transistor.) Then look at the data sheets to find things like turn-on voltage for the transistor, and output voltages for the sensor. Then, you may be able to figure out how to do it. If not, please post those values in a request for more specific help.
Btw: Do you want the motor to run for any particular amount of time, or just for as long as the trigger is triggered? If you want it to keep running after the trigger goes un-triggered, or you want it to stop running after a while even if the trigger stays triggered, you may need additional circuitry -- something like a 555 timer, say.