There is on most cars I've seen a solenoid on the back of the starter motor which when you turn the ignition key acts like a relay and brings in the power to the starter motor. If this is clicking in and your starter motor is not cranking then either your new starter motor is shot or there are serious problems with the engine. If you put the car in gear, take the oil cap off, look inside and push the car can you see the cams moving?
If this is ok, can you get a multimeter set to a range suitable for 12V and check there is 12V between the large cable at the starter motor and earth, also there is 12V between the small wire at the starter motor and earth when the ignition is turned to crank (mind fingers!!!).