When your car is rising, your button shoots out a grappling hook at 45 degrees up from your horizontal velocity. You swing around the grapple point, the length of the rope decreasing over time. (Eventually the length goes negative and starts glitching the fuck out. I may eventually fix this.) You let go of the rope but retain your swinging velocity when you release the button.
When your car is falling, your button initiates a charged jump. After you land, you jump as soon as you release the button. The sooner you release the button, the more vertical the jump will be, but it will always reverse your horizontal direction. You can see your car rotate to give some indication of the verticality vs. horizontality of your jump.
To complete a lap, you must touch all four corners of the track.
Strategy: it's easier to go up the right side than the left. The most reliable way to climb is to grapple repeatedly, releasing the rope on the upswing and immediately grappling again while you're still rising. It helps to also be moving away from the wall you're currently grappling -- this may be difficult after the rope gets too short.