You can use either the demo or the full game to do this, so either way you are OK.
The challenge is:
Launch a manned rocket into orbit, perform scientific research, de-orbit your capsule (you'll need to have a service module to do this, basically fuel and an engine), and land safely in the Kerbin oceans.
Take time to learn the controls with the in game tutorials, and then create a save game and attempt the challenge.
Hard mode: Fly by the Mun and get back to Kerbin.