In KSP, you must build space-worthy craft, capable of flying your crew out into space, without killing them. At your disposal is a collection of parts, which must be assembled to create a functional ship. Each part has its own function and will affect the way a ship flies (or doesn't). So strap yourself in, and get ready to try some Rocket Science!
The game has different game modes, you can play the Career Mode if you want to expand and manage your own Space Center, taking on missions and researching new technologies. Or you can play Sandbox mode if you're only interested in flying and discovering the Kerbal universe without restrictions. There is even a mid point between these two, Science mode.
Stuck and need some help? Check out some of the questions the community have asked relating to this game. If none of these answer your problem or you want to get some tips when it comes to a particular level, feel free to submit a question of your own.