General Tips
When studying using any of the specific strategies described below, you may find it helpful to apply the following universal tips.
Begin with Prayer
Any serious study of the scriptures should always begin with prayer. Prayer invites the Spirit and makes us more receptive to learning. It also helps set time apart from the rest of your day, allowing your mind to enter a deeper state of focus.
In prayer, it's important to express gratitude for the Word of God. Pray to be humble so that you might understand not only what the scriptures say, but also how to liken them to your own life.
Assume Scripture is Truth
The Holy Scriptures (including both canonized texts and teachings from modern prophets) are God's words to us, and should be the standard by which we judge our personal thoughts, feelings, and revelations. This is especially important when we study concepts that may be difficult to accept. Rather than leaning on our own understanding, we should work to align our understanding to the truth revealed in scripture.
"In the mouth of two or three witnesses..."
This is an extension on the previous point. Although scripture is truth, we should also remember, as has been repeatedly declared, that God will establish His word through multiple witnesses. Therefore, a single statement in ancient or modern scripture may not on its own be the source of absolute and eternal doctrine. Elder Andersen taught:
[The doctrine] is not hidden in an obscure paragraph of one talk. True principles are taught frequently and by many. Our doctrine is not difficult to find.
Just as the doctrine is not in an obscure paragraph of a modern talk, I believe it is also not in an obscure verse of scripture. Remember that ancient scripture and modern teachings are analogous, and that much of the Standard Works is simply the recording of sermons or letters that were created by single individuals. But true doctrine, whether taught anciently or in present day, "is not difficult to find".
Read for Original Intent
When studying the scriptures, it is critical that we strive to draw out the original author's intended meaning (a process known as exegesis) rather than attempting to insert our own biases, or twisting the words to reflect what we wish they said (eisegesis). God's words are not meant to always be easy or conformable. They will often challenge us, make us question our personal beliefs, and contradict public opinion. As taught in Isaiah:
For my thoughts are not your thoughts, neither are your ways my ways, saith the Lord. For as the heavens are higher than the earth, so are my ways higher than your ways, and my thoughts than your thoughts.
Using the Key to Understanding
When we read a passage of scripture, whether new or familiar, we should assume as a general rule that 1) the passage means what it says, and 2) that we don't already know what it says. It can be difficult to leave behind our preconceptions, but this is critical to open our minds to greater light and knowledge. In those times when we come across a particularly challenging scripture to understand, whether due to its ambiguity or even apparent contradiction with other scripture, it is helpful to call back to this guideline from Joseph Smith:
I have a key by which I understand the Scriptures. I enquire what was the question which drew out the answer.
No passage of scripture exists in a vacuum. There is always some historical or situational context in which it was given. Particularly for the teachings of the Savior, we should always consider the situation or question that led Him to say what He did, and allow that to guide us toward the proper understanding or interpretation of His teachings.
Assume Each Passage is Significant
We should not lightly dismiss or pass over a section of scripture by assuming that it is not relevant or meaningful. This would cause us to have excessive confidence in our own judgment, and can shut us out from many plain and precious truths contained in verses less traveled. We should assume each passage has significance and was included for a reason, and then we should ask what that reason might be.
Ask Questions
The most importance advice I have received to improve my scripture study is to ask questions. Ask questions of the text, the characters, and the stories. Give preference to questions about specific details over more general and obvious questions which do not stretch the heart or mind.
Ask these questions during every study phase and strategy listed here, and compile your questions. Choose the most interesting ones (while following up on others as able), and search diligently for their answers. You will often surprise yourself with the quantity and quality of the answers you can find. This is how I have received my deepest learnings.