The mind is an entity that comes to be through the processes of several structures (modules) of the brain. It's unknown what all of these structures are and it is unknown how the result (mind) comes to be. This overall system is referred to as "complex".
"A complex system is composed of many different systems that interact and produce emergent properties that are greater than the sum of their parts and cannot be reduced to the properties of the constituent parts." (p. 71) The mind is such an emergent property. In essence, nobody knows how the hell it happens. Calling it an "emergent property" thing probably sounds better.
You don't get an answer to the question "who's in charge?". Well, to be fair, you seem to get a "sort of no one is" (not a quote). The author quotes Luis Amaral and Julio Ottino as follows: "The common characteristic of all complex systems is that they display organization without any external organizing principle being applied". From this quote it's impossible to tell what "external" is supposed to (not) mean. Mr. Gazzaniga proceeds to discuss the workings of the Google ad auction as an example of no one being in charge. As he says, it is run on algorithms, though. I would propose run -by- algorithms and that the algorithms are in charge. Ultimately in charge would be who or what created and put the algorithms in place. If there's no who - nothing of sufficient personal quality - involved, then there is no free will. We'd all be Google ad auctions. The brain's algorithms aren't (fully) known.
You don't get a good definition of the mind. You do get a vague and superficial account of some elements that allegedly are involved in its genesis. Not knowing how the mind is constituted and how it works then leads to uncertainty in regards to free will. In another vague and superficial account, the author briefly outlines that when no exact predictions can be made (chaos theory; uncertainty principle), determinism (the lack of free will) can't be proven.
You also do get some information on the relevance of unconscious processes. Various modules of the brain work unconscious to the/any person in question, come up with individual results, these results may compete with each other and, after having somehow been evaluated, lead to a final result, an effect. This effect can be you doing something or be you not doing something. So, input (information) is processed by several structures within the brain, somehow integrated and then acted on by the organism/person. At any rate, this only comes to your attention/awareness once it's already been decided. The process of evaluation occurs without you being aware of it until it has been completed. Consciousness is slow; unconsciousness is faster.
"When we set out to explain our actions, they are all post hoc explanations using post hoc observations with no access to nonconscious processing. (...) These explanations are all based on what makes it into our consciousness, but the reality is the actions and the feelings happen before we are consciously aware of them -- and most of the them are the results of nonconscious processes which never make it into the explanations."
This passage (on pages 77 to 78) is less than clear and appears to state that every action is decided and made unconsciously. Later on it is modified into "most of our processing is going on unconsciously and automatically". Some time thereafter (pages 128 to 129), he talks about "[the] buildup of electrical charge that preceded what were considered conscious decisions [which] was called Bereitschaftspotential, or more simply, readiness potential". This goes back to the brain initiating actions unconsciously.
Unfortunately, he doesn't elaborate on it enough. Scope and details remain unclear and missing, among them the possibility of inhibiting readiness potentials and suppressing actions. Furthermore, in this context, he doesn`t discuss the intentional acquisition of automaticity, as in training yourself in order to produce a specific unconscious response in reaction to a specific situation (for example learning to play the piano really well: intuitively). Thus he concludes the respective section with these words: "Conscious volition, the idea that you are willing an action to happen, is an illusion. But is this the right way to think about it? I am beginning to think not." In "thinking not", he proceeds to go back to the uncertainty principle/chaos theory and emergent properties. As mentioned above, that doesn't convince.
This book, as far as I can tell, doesn't add anything new to the matters it addresses (the mind, modularity and free will (see above), also nature vs. nurture and, in its final chapter, the relevance of personal responsibility to criminal law). If you are already familiar with a few popular science books in this field, there's not much sense in going for this one. With all due respect to the author, it lacks in depth, clarity, completeness and novelty of thoughts.
On emergence/emergent properties, I would recommend reading chapter 5 (pages 143 - 181) of Terrence W. Deacon's book .Incomplete Nature: How Mind Emerged from Matter (W. W. Norton, 2012) [already available hardcover]. The entire book is relevant.