Stepper Motor control with 1 limit switch

Hi, welcome to the forum.

When the project is powered on, how do you know where the stepper motor is ?

The Arduino Stepper library: https://www.arduino.cc/en/reference/stepper.
Start with this library.

The AccelStepper library: https://www.airspayce.com/mikem/arduino/AccelStepper/

A switch bounces, you need something to debounce the switch. There are a number of good libraries for that.

To detect the moment (the event) when a switch is closed, you need the State Change Detection: https://www.arduino.cc/en/Tutorial/BuiltInExamples/StateChangeDetection.

Some debounce libraries have also the State Change Detection included.

Can you make a first sketch ? Put it between code tags and show it.