I don't often do top ten five lists. This is basically a list of things that most people might find informative about studying the Bible.
1. The Bible is meant to be read aloud. Historically, reading was very hard once upon a time. In Bible times, words were written in all caps with no spaces between words and no punctuation. This made reading VERY hard. You either knew how to read extremely well, or not at all. There was almost no in-between. In the fourth century, we have letters of people saying "hey, I saw a guy just staring at a piece of paper. I asked him what he was doing, and he said he was reading. Isn't that crazy?" And so we know that before the fourth century, everything was read aloud.
More important than history, let's look at theology. God created through the use of his spoken Word. The creative, life-giving Word is something that we don't just read -- we can participate in God's creative Word. When we proclaim God's Word openly, all creation sings with us (this ties in to my view of the Psalms). And, truthfully, reading silently does not allow the rest of creation to benefit and rejoice with us.
And psychologically: when you read silently, you engage visual memory. If you read aloud, you engage your visual memory plus your aural [auditory] memory and kinesthetic [muscle] memory. No matter whether you're a visual, auditory, or hands-on learner, everybody will do better engaging all three rather than just one type of memory.
The Bible is meant to be heard. Reading aloud will also help you ask questions: "who is speaking here: God, or the prophet Isaiah?" "Was this spoken with sarcasm or irony?" etc.
2. The Bible is not naturally separated into chapters and verses. The person who made the chapter divisions, for the most part, did an outstanding job. As for verse divisions? It's been said that he marked verse divisions while drunk and riding a galloping horse. Take, for instance, Jonah 1:1: "And the word of the LORD came to Jonah son of Amittai, saying..." Saying what? That's not even a complete sentence!
The basic unit of meaning in language is the sentence. That is the central level of meaning. Words influence the sentence, and the sentence influences the word even more. The paragraph or section influences the sentence, but the sentence is the central building block of meaning in language. SO, read the entire sentence. In fact, it wouldn't hurt to read the entire paragraph or (if you have time) the whole chapter.
3. It doesn't always come back to knowing Greek/Hebrew. Let me tell you one of the things you won't notice in your English translations: sometimes the original is ambiguous, and we have to make an either-or choice in translating. For example, Better Bibles Blog's Wayne Leman notes the difficulty of 1 Cor 7:36-38. Whose virgin is in question? Is it the virgin daughter of a father, or a young damsel that a man intends to marry? There's no way to translate this ambiguously into English without it becoming awkward English (see the ESV for instance). All communication is, by its nature, both vague and redundant. Strange, but true.
4. It doesn't always come back to knowing Greek/Hebrew. Jesus said that "this generation will not pass away until all is accomplished." But what did he mean by generation? You could go to the Theological Dictionary of the New Testament (which I would do, if I could afford the ten-volume set for $400), or you could just consider how the word "generation" is used in the English translation. It can refer to 1. a contemporary group of people (which is the same as our contemporary use), 2. people of a certain character type, which would be more like a "genus" than "generation." For a use of this, see Psalm 24:3-6 to refer to the "genus" of person who will ascend the hill of the Lord. 3. It has various, lesser meanings also.
5 It doesn't always come back to knowing Greek/Hebrew. If you want to know the main things that differ between the original languages and our translations, I'll cover that briefly. Firstly, Bibles are translated at about the eighth-grade reading level because that is all that most non-college folk can comfortably read at. College grads, on average, read comfortably at the tenth-grade level. Because of this simplicity, sentences are often cut in two to make for easier reading.
Secondly, translations tend to make things seem specific where there may be some ambiguity (this is hard to avoid, as the 1 Cor example shows). A bad translation choice will introduce ambiguity where it is clear in Greek/Hebrew. Sometimes, this can't be easily avoided either, though. "For there is one mediator between God and man, the man Jesus Christ." Jesus' maleness has nothing to do with His ability as a mediator.
So in short:
1. Read aloud, as much as you feel comfortable doing so. Read publicly with friends and family!
2. Read more than a verse at a time. John 3:16 has a different tone to it when you read it in context of the rest of John 3.
3. Read with reverent care. As long as you aren't reading the Cotton Patch translation or Conservapedia, then you are handling the genuine word of God. Treat it accordingly and do not disparage it for being a translation. Wayne Leman said it best:
Some people want absolute certainty about what each verse in the Bible means. Some people want to use a Bible version which they feel gives the correct translation for each verse. But we cannot have such certainties about every verse in the Bible. The biblical language texts are not always clear enough for us to know for sure what the biblical author’s intended meaning was. We must be content not to know some things for sure in this life. Personally, I think God wants to draw us to himself through life’s uncertainties. We can trust, I believe, that he is certain, that he knows total truth. If we try to find total truth anywhere other than in him (including in Bible translations which were done by teams who did their very best, but which cannot humanly know how to translate everything with certainty), we are going to be disappointed. But if we allow lack of certainty about some things, including things in the Bible, to draw us toward the One who knows far more than we do, we will find contentment in knowing enough of what we need to know in this life.