There are a lot of helps you can use to enrich your understanding of what any scripture passage means. Download a (free) resource like e-sword.net.  Or, consult a resource like biblestudytools.com and look at their "Study" tab to access Commentaries (scholars who help with interpretation), Concordances (to find similar verses), Dictionaries (to understand the various terms used in the bible) and much more (there are even videos on specific passages or book introductions).  Don't forget that it's important to remember the Genre (type of writing) when you are trying to understand what a verse means.  The bible is made up of various genres: History, Law, Prophesy, Wisdom/Poetry, Gospel and Letters. 

In general, try using these steps: Observe what the passage is saying, Interpret or discover the meaning Apply to your own life for growth.  See this helpful webpage for more on those steps: 3 Simple Steps for Studying the Bible 

This is a focused way to read and listen to the Lord in scripture.  There are 4 parts: Lectio (read), Meditatio (meditate), Oratio (prayer) and Contemplatio (to contemplate and rest).  For a full explanation of these 4 steps, read an introductory article like "Lectio Divina: Divine Reading" by Brian Hardin or "How to Begin Hearing from God" by Nathan Hale. 

To meditate on scripture is to ponder or focus on God's words in order to let them sink from our heads into our hearts. David made it a practice to meditate on God: Psalm 63:6 "When I remember Thee on my bed, I meditate on Thee in the night watches." You will want to read reverently and creatively.  Try reading the same passage over and over or committing a verse to memory so you can walk or close your eyes while you ponder its truths. There are many ways to meditate on scripture.  I have even done it out loud with a friend while taking a hike. See this short article for 5 different ways to meditate on a verse.