How you want to approach reading and absorbing your texts is really dependant on personal preferences. I would recommend that for your first reading, just read it as you would any other novel. The purpose of your first reading should be to understand the story and the characters on a basic level. Your main goal after the first reading is to be able to recall the order of all significant plot events, have a basic understanding of all the characters and their importance to the story and recognise the novel's central themes.
Identifying key sections, passages or quotes is much easier once you know the sequence of plot events. This gives you a more holistic perspective of the novel meaning you will identify any examples of foreshadowing and character changes more easily. It is much harder to identify what is important when you don't fully understand the plot as you won't be able to place each individual section into context, which could result in over-analysing certain sections or failing to recognise the importance of others.
As for what to look for, start by looking at the major points in the dramatic structure - The exposition (When the characters and setting are introduced), Rising tension, Climax, Falling tension and the Denouement/Conclusion.
Other things to look out for would be changes in character, soliloquys/monologues, any sudden revelations, repetition of symbols/metaphors/imagery, 'thematic' sections (sections that, rather than advance the story, explore the novel's themes and ideas), social commentaries and any authorial values communicated through the text (For instance, any messages that the author is trying to communicate to the reader).
The next step is to look at what the author is trying to communicate to the reader and the ways that he/she does that. For example, is the author criticising an aspect of society? If so how? A character may represent society as a whole or a social attitude. Being able to look beyond the scope of the story and consider why the story was written in the first place is pivotal to writing a thorough and comprehensive textual analysis.
Also don't worry if there are aspects of the novel you don't quite understand or sections that you know are important but don't fully know why. It is still early in the year and you are yet to have discussed the novel in class. Class discussions will often reveal alternate perspectives that you had not previously considered or help to clarify your own ideas.