Before talking about the different ways how you can study the Bible, it's helpful to first distinguish what you can study. As has been mentioned, you can do topical studies, whole Book studies, character studies, etc. So how are the different approaches to studying the Bible?
Personal/Devotional Study has less emphasis on "study" and is more focused on meditation and reflection. It's using the Bible to nurture you and your communication with God as you spend time with reading his word and in prayer. People also call this "Personal Quiet Time" or "Devotions".
There's deductive and inductive Bible studies. These two approaches are the opposite of each other, but it's helpful to talk about them together to compare how they are different.
Deductive Bible study starts out with a basic premise, topic, assumption, objective, or conclusion and you find supportive evidence to prove the basic conclusion. Topical studies utilize the deductive method: You pick a topic (e.g., "Love") and you look at the passage that talk about love. Deductive Bible studies are the method used in lecture-type studies where the Bible study leader is regarded as the "expert" leading the class in the direction to the objective/topic of the study. The problem with deductive study is that it's too easy to get railroaded and take things out of context. Whatever you do, don't simply look up words in the concordance to pick and choose verses without first reading the entire context of those verses.
Inductive Bible study is the oppositive of deductive study. You start out with no precepts or assumptions whatsoever, and that's how you approach the passage of study. You observe, ask questions, and formulate interpretations and applications based solely on the passage with no preconceptions. In this way, you examine the evidence (Bible passage) first before you draw your conclusion. This approach is much more conducive to active participation by the whole Bible study group and the Bible Study leader is merely the facilitator of the discusion. But this approach takes a little getting used to and is best learned in a group before tackling on your own.
Another way to look at the differences is that in deductive study, you are following someone else's study (because someone had to do the study to put together the study), and inductive study is where you study and learn on your own.
And if you want to really seriously study the Bible, try an expository study. This method takes an inductive study approach, but is more indepth as you look up original meaning of words, historical & cultural contexts, and other reference materials.
A note should be made about reference materials. A good concordance like Strong's Concordance is the second essential book next to your Bible for any type of Bible study. A lot of people become fanatical about a particular Bible translation, but in the end they are ALL still translations. It can be helpful to look at different translations in your study, but unless you can read ancient Hebrew and Greek, a concordance will help in original meanings of words. Next to Strong's concordance, Vine's Expository Dictionary is also highly recommended. Following that, a Bible dictionary or two can be extremely helpful too as they can give background information. One of the first reference material people turn to are commentaries, but they should be the very last things you look at. Yes, commentaries can give you insight on passages that you never would have considered, but they are still just another person's interpretation. Regard commentaries as just that--another person in the room contributing your your study, but NOT the definitive authority.