Fortunately a great deal of ancient literature has been translated into English.  Many works, like the Bible or Homer's Iliad, have multiple English translations for you to choose from!  Even with translations readily available it can be very helpful and enriching to learn to read and interact with the texts in their original languages.  For some ancient languages (like Latin) there are plenty of opportunities to take classes.  For others (like Ge'ez or Syriac) you're unlikely to find a course at your nearest university.  But that's ok -- there are resources available for the dedicated and courageous autodidact!

[NOTE: We'll be adding more language postings over the next few weeks! So keep checking back]

[UPDATE] I just found out about Lexicity, a website with online ancient language resources.  Be sure to check them out!  You may also find The Cambridge Encyclopedia of the World's Ancient Languages useful.