Common problem, but with many possible causes. Before going down the road of expensive and difficult replacing of the motor itself, the order of testing is as follows:
1. Ensure Battery is fully charged and cables firmly connected
2. Try to start with bonnet and driver window open (so you can clearly hear for any clicks and thunks)
3. If you hear a click and thunk, followed by only a loud click after successive attempts the motor may be working but stuck in a partially engaged position. For Manual Gearbox engage first gear and reverse in succession and rock car back and forwards to free starter. For automatic gearbox (with key out of ignition), turn the engine over with a 20mm Socket head on the bottom centre Belt wheel (front of engine). Anti-clockwise is the normal direction of turn. If it is stuck solid it is an engaged or problematic motor gear head, then try to turn 3 complete revolutions clockwise, followed by 4 complete revolutions anti-clockwise (it should now turn where previously it was stuck). This can be done from under the car but it is easier from top with fan removed. This will free any engaged or partially engaged motor. Try to start again ( no need to replace fan until you are sure the car starts).
4. No clicks or thunks - Starter and solenoid not operating - check all connections, fuses and relays. (solenoid issues are dealt with elsewhere on this thread)
5. removing the starter motor itself, with its housing is problematic, as the inner of two securing bolts is difficult to reach. however, by removing the rear end plate, Bearing base and connections from the starter housing, the actual motor and assembly can just be slid out.