I was thinking about making some sort of tutorial, but ran out of time. Wall clipping is done by using X-ray mode and grappling to a hold point that is behind a wall. Your WASD movement is not able to clip through walls. Be careful while using X-ray though, as hazards turn invisible with the rest of the level, and there is a malevolent bot that will chase you through the last two levels.
To clarify, WASD is relative to your looking direction. If you're looking straight down, then W is down and S is up. Vice versa, if you're looking up, then W is up and S is down.