To put it simply, our hermeneutic (her-meh-new-tik) is the set of principles we use to interpret the Bible, and there are various hermeneutics that Christians might apply depending on their understanding of Scripture and its inspiration. Many Christians have at least a vague sense of the principles they apply when trying to understand what a passage from the Bible means, but a lot of us would benefit from developing a greater appreciation for the various aspects that go into well-rounded Biblical interpretation.
For example, most evangelicals would tend to agree that "the Bible should be interpreted literally." This is a hermeneutic principle. Usually it's applied when reading the first chapter of Genesis to understand that God created everything in the span of 144 hours (affirming that God's work of creation was completed in exactly six of our calendar days). Or it's applied when reading the closing chapters of Revelation to understand that Jesus will establish a future global monarchy on the Earth, which he will rule for exactly 1,000 years. These interpretations are applications of an "interpret the Bible literally" hermeneutic principle.
However, the same evangelicals who apply the literalism principle to these passages know that it shouldn't be applied to other passages:
But I say to you that everyone who looks at a woman with lustful intent has already committed adultery with her in his heart. If your right eye causes you to sin, tear it out and throw it away. For it is better that you lose one of your members than that your whole body be thrown into hell. And if your right hand causes you to sin, cut it off and throw it away. For it is better that you lose one of your members than that your whole body go into hell. Matt. 5:28-30
Would anyone today say this passage should be interpreted literally?
The problem with having only a vague sense of hermeneutic principles is that we're unsure when to interpret a passage literally and when to allow some leeway. Most of the time we end up simply "going with our gut" (or "letting the Spirit lead" if we want to spiritualize our inclinations a bit). Sometimes we're simply adopting an interpretation that suits a personal preference.
Fortunately, it is possible to develop a more formal set of interpretive guidelines that we can apply to our Biblical studies. Posts on the Hard Pursuits blog will include a hermeneutics tag when they involve a particular principle that aids in interpretation. For instance, remembering that parables are not meant to be interpreted in a literal sense or using Scripture to interpret Scripture are two hermeneutic principles that help us understand the Bible.
If you'd like to start developing your own hermeneutic, I'll suggest the following books (they are listed based on the order in which I read them, not from most to least helpful):
How to Read the Bible for All Its Worth
by Gordon Fee and Douglas Stuart
Fee and Stuart provide a solid introduction to hermeneutics for the average lay person. Each chapter covers different types of Biblical writing, such as New Testament letters, gospels, and parables, and Old Testament narrative, prophetic writings, and wisdom literature. While the principles offered are sound, there is some obvious bias as it seems Fee uses every opportunity to advance his understanding of women's roles in ministry. (Personally, I think Fee fails to fully apply some of the principles he advocates on certain texts.)
by R. C. Sproul
Sproul's book is broken down into six sections including discussions on private interpretation, rules for interpretation, cultural considerations, and tools for Bible study.
How to Read the Bible as Literature
by Leland Ryken
Similar to the other books listed here, Ryken encourages us to consider the Bible as various forms of literature. He breaks the Bible's content into stories, poetry, proverbs, gospels, parables, epistles, and visionary literature.
There are plenty more introductory hermeneutics books, but these are all very accessible for the average lay person and share a Protestant, evangelical understanding of Scripture. You will find considerable overlap in their content, which should reassure you of the validity of their content. Fee is Pentecostal; Sproul is Presbyterian; yet they find common ground in many of their interpretive principles. Though the principles don't prevent considerable theological disagreement, they at least provide a shared foundation upon which to build. Eventually, you can begin looking into more advanced hermeneutic principles and consider how different hermeneutics have been applied through church history.
As you develop a more precise hermeneutic (e.g. we only read the Bible literally when it was intended to be taken literally), you will likely find some parts of the Bible become more understandable than ever before. On the down-side, you may find yourself starting to disagree with some of your favorite authors and teachers. This can be especially discouraging if you begin to see that your pastor regularly misunderstands the text he's preaching. Be assured that your actually learning to hear God speak more clearly through His Word.