How do you make a push button maintained on a starter?

You add an auxilliary normally open contact to the contactor. This contact will be closed any time the contactor is energized. Wire the contact in parallel with your start button. It works like this: When you push the start button, the contactor energizes, starting the motor (or whatever you are controlling). At the same time, it closes the aux. contact. You can now let go of the button, because the aux contact is holding the circuit energized for you. Of course, now the load will run forever, so you have to add another button to break the circuit, allowing the contactor to de-energize. The start button is normally open, closing when you push it. The stop button is normally closed, opening when you push it. Most starter contactors have auxilliary contact kits that you can buy just for this purpose.