Lucene's StandardAnalyzer includes a StopFilter that removes some typical stop words from anything passed through it. The standard list of english stop words is pretty short; some articles, pronouns and prepositions, mainly.
If you wish to define your own set of StopWords, the StandardAnalyzer has a couple of constructors allowing ou to pass in your own set of stop words, and particularly, this one. Simply create a CharArraySet containing the desired stop words, and pass it into that constructor and your on your way.
I believe most other typical analyzers have a constructor accepting the same arguments as well (at a glance, it looks like almost all of the language analyzers in analyzers-common follow that pattern)
Of course, be sure and use the same analyzer for both indexing and searching.