Arrow keys. While on a wall, press the up arrow key to wall jump. Only the black parts are platforms/walls.
Credit to @griffpatch_tutor's Platformer Tutorial for almost all of it. I had it made all by myself before, but his tutorial helped me completely revise this to make it better. But what wasn't by him...the wall grabbing/jumping! That was 100% by me (except that it's designed to work with griffpatch's engine), and I'm pretty proud of it. If you want to use this engine, please give credit.