When saying "fully understand" the book, I mean how many times will it take to be able to understand every little detail and important topics and quotes/lines from the book.
It's either one or it's infinity, depending on how much understanding you are looking for.
Anyone who reads the book relatively carefully once can understand the basic ideas of the book. This is especially true if you have questions to guide you as you read. It is not hard to understand the basic themes of the book.
However, it would surely be impossible to remember "every little detail" and to have quotes for every possible theme. I would bet that most teachers who have taught the book over and over would not even claim that they have that level of understanding of the text. I also imagine that they would say that they never could gain that level of understanding no matter how many times they read the book.
To Kill a Mockingbird is one of those books you simply cannot read only one time. In any book that strongly features symbolism and foreshadowing it is important to read at least twice. I would suggest reading more often, but I know that is likely to be unreasonable for most students. If you cannot read a book twice, it is a good idea to read summaries and analysis of the book, such as those available on enotes, before or as you read. Although this many ruin some of the joy of the book, it will give you some of the benefit of multiple re-reads when you only have time to read the book once.
To really understand this book, you have to be able to pick up on the nuances of language and the foreshadowing the author uses throughout. You will not notice these the first time you read the book, because when we read a book the first time we tend to focus on plot and details of characters. These things are important, but when we already understand them we will get more meaning out of the story. As we read a book the first time, we get a feeling in the back of our mind that something may be important but we really do not know until we finish the book. That is what foreshadowing is for—authors hint for careful readers, or readers who are reading the book again.
If you can’t re-read a book, another option is to read the book once and then read all of the summaries, critical analysis and criticism that is available. Since you are already here at enotes, you have all of that at your fingertips. It will not be quite as good as reading it beforehand, but you will still develop a deeper understanding.
Your question makes me smile, katemckay, when I think of all the books I've read numerous times to fully understand them. The truth is, I'm not sure a really profound novel will ever be fully understood, since our understanding of it changes as we change. I read To Kill a Mockingbird about every ten years, and each time I read it, I find meaning that had escaped me previously. The book had not changed, but I had. That being said, I think what you are referring to really is a mastery of the novel in terms of its literal content and perhaps literary elements, such as theme and symbolism.
To understand the setting of the novel, the Deep South (Alabama) in the 1930s, some research of American history would be helpful--not necessarily the history of events, but the historical time: how people lived, how they dressed, the cars they drove, the social values they adhered to, what was happening in the world, etc. Understanding the time period would help you understand many specific references in the story.
In terms of its literary content, your understanding of this will grow as you develop your own literary skills. Reading the novel three times in a row, for instance, won't develop immediate understanding.
One way to develop a greater understanding of the novel, or any novel, is to keep a journal while you read. Write down references or passages that you don't understand and follow up on them in class or through some independent research. You don't have to understand every detail to understand this novel, but clearing up the "unknowns" will make it more meaningful overall.
I'm including some links below to several eNotes references that should be helpful. There are many others on the site. Good luck and keep reading. Also, read To Kill a Mockingbird again in ten years.. You will be amazed at what you find in it that does not speak to you right now.