Never ever heard a single opera? you'll have to start somewhere.
But where?
Preamble for non-musicians: if you're occidental you live in a world that is soaked with tonal music. Tonal means roughly everything that's in the commercials, everything that's in the movies and almost everything from the XVI-XVII century to the beginning of the XX. As every definition, borders are a lot blurred.
Tonal means, technically speaking, centered on one note of the scale, which is the most important, the one which begins and ends the whole work, but also a note where the piece goes frequently. Ever heard "oh, yes, this song is in B flat major"? B flat is the tonic, which communicates calm and quiet. There is also another important note, which is the dominant, the fifth degree of the scale - in our example it's F - which conveys a tension feeling. Try to play F + A + C, then F + B flat + D on a piano to get a rough idea of what we are talking about.
We are educated to a music of this kind from our birth (lullabies and such), so everything different seems strange, awkward and ugly. I will never advise a beginner to start from Alban Berg's Wozzek, a real masterpiece, only because of that fact. He'll get there step by step. Instead, if you have a little child, make him listen to everything, from Monteverdi to Varèse, from Josquin Desprès to Petrassi, and also to other things, if you find more - I have a cd full of ancient Greek music which is wonderful - but I'm going astray.
We can like almost everything we can get to understand. Opera is less popular than cinema mainly because it's a little bit more complex than an action movie, but it's also a lot more rewarding in the long run. If things are too simple we soon get bored. And complex is not complicated. Men are complex, life is complex, school is complicated;-). And guess what would life be if it was simpler...
Like everything, we must find our own route to get to his heart. One could start with Puccini, another with Verdi, another with Debussy. Don't stop if you don't like an author. If you hate, say, Ang Lee's films (just an example), maybe you'll like Lucas' or Fellini's.
The first operas you should buy - in cd or dvd, it's better to avoid tapes because of the terrible sound quality - should be enough varied to make you aware of all or at least a great part of the alternatives. Then you'll deepen you research starting from the period/author/genre you liked best.
Keep in mind that if you have little time, you can buy cds and listen to them when you do other things: don't you know that music improves concentration? Otherwise you can buy a score and listen to the cd reading the music, if you're able to, or you could buy the libretto, which is especially useful if the opera is in a foreign language.
Even better, buy a DVD, with subtitles and all the action on the stage. It's like a movie, for those who never watched an opera, and it' real fun.
But best of all, go see some operas live.
Here are some authors and operas you can start with:
early XVIII century
Georg Friedrich Haendel (or Händel, it's the same)
Rinaldo, Giulio Cesare
late XVIII century
Wolfgang Amadeus Mozart
Die Zauberflöte (The magic Flute), Le nozze di Figaro (The Marriage of Figaro), Don Giovanni, Così fan tutte (Every woman does the same)
early XIX century
Gioacchino Rossini
Il Barbiere di Siviglia (The Barber of Seville), La Cenerentola (Cinderella)
Gaetano Donizetti
L'Elisir d'amore (The Love Potion)
Vincenzo Bellini
Norma
mid XIX century
Giuseppe Verdi
Nabucco
Richard Wagner
Lohengrin, Die Walküre
late XIX century
Giuseppe Verdi
Traviata (The Corrupted Woman), Rigoletto, Trovatore (The Singer), Aida, Simon Boccanegra, Falstaff
Giacomo Puccini
La Bohème, Tosca
Georges Bizet
Carmen
Modest Mussorgsky
Khovanshchina
XX century
Giacomo Puccini
Turandot
See if you can find something you like. I think a selection like Rossini's Barbiere di Siviglia, Donizetti's Elisir d'Amore, Verdi's Rigoletto, Mozart's Don Giovanni, Puccini's Turandot, Wagner's Walküre, and Haendel's Rinaldo (I think the order is also good, just bear in mind it's not chronological!) will give you a good panoramic on what opera has to offer, bearing in mind that opera was "invented" in 1500, and that there are still composers writing operas.
I tried to keep this list small not to confound newcomers. I'll expand it elsewhere. Come back when you've done your homeworks;-)
Good listening!