Kind of like Batman.
The story starts in the present with Desmond and the gang going to a certain spot to set up the Animus. I won't say where so you can be surprised if you haven't played it yet. The past story starts where 2 left off. Basically the games plays like 2, looks and feels like 2 also. The story is the Borgia take control of Rome and Ezio recruits new Assassins to help bring down the Borgia. One cool thing I liked was how you get to rebuild Rome. I know 2 had something similar, but in this game you can pay to restore buildings and make Rome more and more Templar free. I say this is kind of like Batman because like Gotham City Rome is corrupt and needs a hero. Ezio is that hero like Batman and he has a whole family of Assassins just like Batman does with his sidekicks. Also like Gotham Rome has corrupt officials. One really cool thing is once you kill a Borgia captain you burn the tower and turn it into an Assassins tower. Also the more buildings you buy the better Rome gets. So not exactly like Batman, but similar.
In terms of progression of the first civilization storyline it involves looking for the Apple and the ending is close to being as good as the ending of 2. Basically just go into this thinking of it as a long expansion to Assassin's Creed, but don't consider that a bad thing.