The game starts out with a very cinematic overview of the previous events as told by Desmond's father – and as he works his way through Desmond's story (skipping a lot) you get a general sense of the situation – enough so that if this is your first exposure to the series, you can follow it. The details of the Animus are offered, with an Introduction to the Templar and the worry that if their plans cannot be stopped, it may very well mean the end of life on the earth as we know it.
The tie-in with the whole end of the world on December 21st is rather cool - if you did not catch it it is a reference to the Mesoamerican Long Count calendar that ends on that date that was created by the Mayans. The theory is that all sorts of nasty alignments are going to take place on that date, and time will end. It will suck if that is true, since we will never get to play Assassin's Creed IV but I have my doubts that it is really that big a concern.
After the voice-over Introduction completes, we find ourselves (as Desmond) in the back of a van with some of our compatriots, heading for some unknown location, and you might notice the glowing thingy in his pocket, yeah? That - if you played the previous games - is the fabled Apple, an immensely powerful artifact that has the power to bend reality itself.
When the van arrives at its destination you go into a cave and, using the Apple you activate some carvings that are really a mechanism or machine inside, and a passage is opened that leads to yet another door and passage that, once he opens it, Desmond decides is their destination.
As you move through the second door you end up sliding down a slope, your chemical light stick coming unattached to you as you slide to the bottom – you move forward into the ancient ruins to find a glowing cube on the ground - the switch that when inserted into the proper slot powers up this ancient site. As the power comes on Desmond starts to have memory bleed - memories from your ancestor forcing their way into your consciousness.
Your mates placed you in the Animus, and you learn from your father that the Temple you are in was communicating with you - you confirm that you learned what you are seeking: the Key. Concluding this conversation initiates your first mission, which is to complete the tutorial on movements and attacks in the loading area of the Animus. To do this you need to follow the on-screen and voice prompts, head after the green marker, and not screw up!
When you get to the end you will be scored out of a possible 140 points and unlock your first Achievement in the game: “Rude Awakening” (10G) Re-Enter the Animus.
That completes the tutorial and you are ready to enter the first Sequence!