1. UNDERSTAND - What does the passage actually say?Notice that the proportion of this that is "spooky" or "mystical" is very small. For example, in understanding the text, there is nothing that is done when reading the Bible that we don't do pretty much automatically when we read any book. In the explanation section, the only assumption that we are really making is that it is reasonable to work on the basis that the book has a unified message. If it doesn't have a unified message, then we would expect this process of explanation to break down.
1.1 Form - How, or in what form, was the passage written?
1.2 Words - What is the meaning of individual words?
1.3 Context - Where does the passage fit in the structure of the book?
1.4 Purpose- Why was the book or passage written?
1.5 Setting- In what situation or for what situation was the book or passage actually written?
2. EXPLAIN - What does the passage mean?
2.1 What is the main point or teaching of the passage?
2.2 Where does the passage fit into the Bible's overall message?
2.3 How does the passage compare with other Bible passages?
2.4 What general principles or theological truths does the passage set forth?
3. APPLY - What does the passage mean today?
3.1 Is there a warning to be heeded, an example to follow, a command to be obeyed or a promise to trust?
3.2 Is the main point of the passage some teaching about God or human beings or the church?
3.3 What is the equivalent situation today to that of the original readers?
3.4 Does it lead to prayer or praise?
4. UNDERSTANDING THE BIBLE - a summary
5. The role of the Holy Spirit
The "apply" process is accepted by Christians because they believe that the Bible is not only a text addressed to its original readers, but also a message from the God who created the universe to anybody who reads it throughout history. That sounds like a pretty startling claim, but in justification of it, I would refer people to a short essay by Francis Schaeffer called "Is Propositional Revelation Nonsense?" A quick search has failed to find a copy of it on the internet, but here's a link to a post from somebody else who discusses the essay and introduces the main points. I also referenced it here.