I don't know how to implement jumping into my script.

Tons and tons of tutorials out there for first person controllers with jumping, so it doesn’t make any sense at all for one of us to retype one of them for you here. Google Youtube for more.

I see you’re using a rigidbody above, but if you would be happy with a simple character controller mover, here is a super-basic starter prototype FPS based on Character Controller (BasicFPCC):

That one has run, walk, jump, slide, crouch… it’s crazy-nutty!!