I am a non-theist who is certain that the Bible is not the word of God, even if a "God" did exist.
And yet, I study parts of it from time to time, I am interested in such stuff, not just Biblical.
I approach it as I would any writing from a particular time. I find out what the times and morals and beliefs and political situation was at the time the writing was probably done. I read with interest the latest scholarly views, preferably from scholars with no real axe to grind, especially as to date of writing.
So , early O.T stuff is approached very differently to N.T stuff.
With the N.T , I realise that the writings of Paul , and those of deutero-Paul, pre-date the Gospels by some years, divided by the shattering events of 70AD,
so , the post Temple world of the Gospels must be read differently from Paul or "Paul", and so on.
I do not see the Bible as a source of Truth or Wisdom to any great degree, though some truth, and some wisdom is therein, as with most scriptures, but each book, and sometimes parts of books (1st and 2nd Isaiah for example) are interesting writings of their time.