A friend of mine introduced me to this through his letsplay video:
Not a tutorial, since he fast-forwards through all the meaty bits in favor of the cool looking flashy bits. But as a game introduction, I thought it was great. I made it a whopping 1:50 before I started trying to find the game.
Get it here for $23 ($25 if you also get the Kerbal-maker app). I don't think the app is worth $2, but whatever, the game more than makes up for it.
A lot of the science is done for you, so you don't need to be a rocket scientist to get stuff in the air... but I would imagine it would help, especially with docking (hard as hell). You build rockets and aircraft and fly them. I highly recommend doing the tutorials first, though unless I missed one, they missed one VERY helpful tool: the Orbital Maneuver tool.
Once you're high enough in space that you have time to use it before you come crashing back to earth, you can set up maneuvers, which help you figure out how long to burn at which angles to set up the orbits you want. You simply click on your orbital path (usually a light blue line/ring) and select "Create Maneuver" then adjust each of the directions you think you might want to burn in until you get the projected orbit you want (Dotted line/ring). It will show you the direction you need to burn on your navball with a blue marker, with the required burn time along the right. You should do it while watching the map, though, so you know exactly when you want to cut out.
So far I have managed to put three space stations in orbit, and I've gotten progressively better at it each time. Eventually I hope to move one out to the moon and build the other two into refueling/construction waypoints. Oh, and I also smacked a lander into the moon. I didn't land; I ran out of fuel to decelerate. But I hit it, which is progress.