Astrokid cannot jump, only go up and down stairs. His goal is to reach the blue sky portal to pass the level. You'll find in the game different kind of terrains, aliens that you can push and much more, as well as a comprehensive tutorial that will explain you what to do in each stage.
Arrow keys left/right to move horizontally; arrow keys up/down to go up/down stairs. An easy tutorial will guide you in the first stages. You always can click 'play' to skip the tutorial and go on with the game.