Start at the beginning, in order, without skipping the preface or Book I. The Brothers Karamazov is not the easiest starting point for someone who has never read Dostoevsky, but whoever decides to start with it can do so, as long as they do not change the order of the books.
Book I is slow on purpose. It is prehistory told by a chronicler: two marriages, three sons raised by other hands, and the monastery where the youngest goes to live. It is there that the narrator defines the hero, the family and the elder, and whoever skips it reaches the scandal in the cell without knowing who each person is. The book truly takes hold in Book II, with the meeting in the cell, and does not let go.
If you prefer a shorter doorway, the author's other novels serve better: White Nights, Notes from Underground or Crime and Punishment. They bring, on a smaller scale, the guilt, the shame and the idea that becomes act, which The Brothers Karamazov develops on a larger scale.
A good plan is the 12-week schedule, about 11 pages a day, which breaks at chapter ends. Two things help: keep the names of the three brothers and of Smerdyakov in mind, and read Book V, the one about the Grand Inquisitor, without haste. It is there that the chapter many people know from outside the book appears, and that Book VI answers.