Perhaps the best way to get started with a word study is to compare several English translations of the Bible.
There are dozens of English translations, and each of them is usually the product of a team of translation experts. Chances are that if you notice differences in word usage or meaning when comparing translations, it's a good indicator that the underlying Greek or Hebrew words can be understood differently. These are the words or phrases that you'll want to focus on when trying to interpret the text.
The easiest way to compare several English translations is by using BibleGateway.com. You can compare four translations. I recommend comparing a few of the following translations:
In this example from John 1, notice that some words are agreed upon among all the translations, but they still are important enough that they need to be studied further. For example, the term "Word" seems simple enough, but it carries a lot of meaning. The Greek term behind "Word" is λόγος (logos). This term gets used in a variety of ways in the ancient world, and has an important place in philosophical schools such as Platonism and Stoicism. That kind of depth to a simple word makes for a good word study!
The best initial way to find the meanings of biblical words is to use a Bible study website. There are many websites that offer English biblical texts enhanced with the underlying Greek or Hebrew texts. Here are some of the ones I recommend for word studies: