Break the word into its constituent parts. Many words are aggregates of two or more other words or word parts. For example, the word "breakfast" is actually a compound word made up of the two words "break" and "fast." The original meaning is that when you rise after a night's sleep to eat you are breaking your "fast." Many words have either a prefix or a suffix that, when separated, help to clarify the root meaning of the word. Some words have both, such as reconstruction. Here, "re" means to do again, "construct" means to build, and the "ion" suffix means the process of carrying out the action. Thus, the word means building something again.
Use a dictionary or thesaurus. Most dictionaries have entries that explain not only the current meanings, uses and construction of a word, but also the linguistic origins of the word, also known as its etymology. Often, this will show not only the root of the word, it will also reveal previous meanings that have fallen into disuse as the language has changed.
Go online to WordExplorations.com or Phrase.org, which specialize in words and their meanings. These often go beyond mere definitions of the words to provide an in-depth analysis of the word in question.