I am what you would call a casual player - and it basically took me about an evening to get used to the interface, rules, etc. Not as easy as a FPS though - it will take some time to adjust.
Since I am familair with TBS games, I was up and playing in less than an hour or so regardless, and used the manual and the tutorials (movie style - not interactive) to help me figure things out as I was playing. I play in a windowed mode so I can keep the pdf version of the manual open, and ran two instances of the game so I could keep referring back to the manual and tutorials as I was actually playing without stopping the game.
If you are used to Civ style TBS games it should not be hard to grasp the basics...mastering it is another story - I've been playing for a week and feel like I have just scratched the surface. Definitely a "just one more turn" experience.