Not really build it - you mean explain how it could be done? Or are you going to build a miniature version?
Nowdays the control would be done with a PLC. It could be done with "relay logic" - that's how they used to do it - I expect.
The complete system is going to be quite complicated. Start by listing your inputs:-
Call buttons on each floor
Proximity sensors on each floor - to detect that the lift is there
A button panel in the lift car - minimum 4 buttons - one for each floor
And outputs:-
Motor forward
Motor reverse
Acknowledgement lamps in all buttons
Start with a simple relay "hold" circuit: Energise a relay using a button. A contact on the relay takes over from the button and holds the relay energised. The relay is de-energised by another relay opening a contact...