Very simply hit the launch pad and you’ll be flung across the gap and towards the exit at the end. Hit the red switch and it’ll drop a Companion Cube onto a launch pad behind you.
You need to hit the launch pad on this side to take you back over to the other side. You don’t need to catch it on this pass as you need to come back again anyways (but if you can it’ll save you a bit of time).
The time to hit the launch pad is just after the Companion Cube has hit its own launch pad and is about to start its ascent again. Follow its path as you jump towards it and press the action button to grab it.
Now simply place it on the red button to open up the exit.