Alpha Centauri is a HUGE game with incredible depth - the nearly 250 page manual is a testament to this. That in mind, the designers did a brilliant job with the interface. Mind you, I had never played the Civ games, but after about an hour or two putzing around with Alpha Centauri and the in-game "tours," I had all the basics down pat. It's best not to delve into the manual too much before you start playing. Simply use the interface tours within the game, and these will do a fantastic job of explaining what all the menus and buttons are for. I'm not going to lie - it will take some measure of patience because there's so much to cover, but the effort will be well worth it. Civ veterans will probably be able to pick up the game right off the bat because a lot of interface mechanisms are carried over from the classic.
The left menu works like the Windows Start button
giving you access to all commands
The main viewscreen shows a world view with all your bases and units outside of bases. Clicking on squares will intuitively yield information about that square in the bottom tool bar. Likewise, the same thing will happen if you click on a unit. You'll also be able to see the rest of your units in "the stack" - that is, if several of your units or friendly units are sharing the same grid square, all will be listed in the tool bar. The best part of the interface is that any conceivable command is doable from graphical menus (brought up by right clicking or using the game button on the left), or from keyboard shortcuts. Only the hardest of the hardcore players will be able to remember most or all of the keyboard shortcuts, but it's nice to know they're there.
Right Clicking a unit yields another set of menus
There are various submenu kind of interface screens. Notable among these is the city view interface. From here you're given a zoomed in view of your city and the surrounding squares. Manage the cities yourself or allow the AI "governor" to do it according to 4 different modes of management: Explore, Discover (research), Build, or Conquer. You'll also be able to see how your city is using and managing its resources and production and easily change these things from the interface screen. Further submenus are available from here, like the unit menu and design workshop (more on this one later). These too, have the same intuitive design as the rest of the interface. If you ever get stuck, help is always available from the menu.
The best part is that the bottom toolbar gives pop up messages every turn regarding what is going on with your bases. In the beginning with few bases, this isn't really an issue, but towards the end of a game when you have dozens of bases, this update list is critical to management and a helpful tool.