I've spent most of my adult life convinced that the Council of Nicaea chose what books made it into the bible. And recently learned this isn't true. But this feels like a very common misconception, where did this come from and what is the truth?
This is a complex question. I'll try to address each part briefly, then bring it together.
Firstly, Dan Brown, being a widely read fiction writer, certainly didn't skimp on bending the truth regarding religious practice. In this case, the First Council of Nicea discussed a number of topics that impacted the practice of Christianity going forwards, most notably the titular Nicean Creed, which is a series of statements of belief used by Roman Catholics to summarise the core beliefs that define them as Catholic (as opposed to other denominations of Christianity). Given this, it might be natural to assume that something as central as the contents of the bible would also have been sorted out at this meeting, but that isn't, of course, the case.
'The' bible is also something of a flawed concept, as many branches of Christianity have bibles which contain or exclude books found in others (Protestant bibles have 66 books, Roman Catholic 73 and Ethiopian Orthodox 81, to name a few), and the matter of which to include has caused schism and argument (scholars might prefer the term 'discussion') almost since Jesus' time.
A few key criteria used to decide which books are more authentic than others include authorship (was the author believed to be someone close to Jesus, for example a disciple), antiquity (general historical practice for documents is that things written nearer to the source event are more accurate than those written later[this doesn't mean they are free of bias, of course]) and orthodoxy (does the text conform to current Christian teaching). This last is pretty subjective, as you can imagine.
There is another criteria, that of verification, which can be tricky both for the age of the source events and the religious/metaphysical nature of some of the topics discussed, but has been used to roughly date and order some of the New Testament documents.
Others may wish to expand on this point, or others; Suffice to say the contents of any given bible were never settled (to everyone's satisfaction) by a single meeting or council, and were assembled by various groups to support their beliefs at the time.