ADVICE: One joystick controlling two motors

I am designing and manufacturing a crane for my thesis. I want it to operate with a motor on each of its axes and a fourth motor to open and close its claw. So far I have only been able to find examples of arduino programs online of one joystick controlling one motor. What would be the correct program code for this arduino?

Saying

I am designing... for my thesis

is incompatible with asking for:

the correct program code for this arduino

But apart from that, you should look at a couple of things to help you get started with motors. This explains direction and speed control of DC motors and this is about controlling a servo with a pot. If you get a joystick like this one you can easily manage two servos at once, and maybe use the button as the claw release.

Over to you.....