Breathe correctly. Not only will this allow you to control your breath properly, but it will also improve the sound that comes out of you. When most people breathe casually, they only pull the air into their chest without using their diaphragm. Breathing with your diaphragm is crucial. This is the muscle at the base of your lungs that expands them. To make sure you're breathing correctly, keep your posture straight and place your hands on your abdomen. When you inhale, your stomach should rise, not your chest.
Figure out which kind of voice you have. Basically, if you're a man with a very deep voice, you're a bass. Men with higher-pitched voices are tenors, and those with ranges in the middle are baritones. Women with high-pitched voices are sopranos, while those on the lower end are altos. The kind of tone your voice has also determines which kinds of arias you can sing. If you have a crisp, clear tone, you are probably better suited to comic parts. With a gruffer tone, you might be better suited to more dramatic roles.
Figure out what all of those dots and lines mean. This doesn't have to be as hard as it sounds. There are many websites and books to help you. It might help to get sheet music for arias or songs you know and follow along to match the notes on the music staff to the sounds you're hearing. Opera singers must be able to learn new roles quickly and understand the opera's score, so being able to read music is important.
Listen to as many recordings of operas as you can and sing along to get an idea of the arias that suit you best. In addition to getting an idea of what your voice can do, you'll memorize the melodies, making it easier to learn to read music.
Practice scales daily to strengthen your larynx and build muscle memory. A baseball player does the simple mechanical work of taking batting practice and lifting weights, so you need to build your vocal muscles by singing through scales. Start with the standard C scale (think "Do Re Mi," the song from "The Sound of Music"), then repeat, singing the scale a half step higher.
Hum different vowel sounds while modulating a note as high and low as you can comfortably sing. According to "Become A Singing Master," you should keep your lips loose while you do this. That way, your throat, lungs and diaphragm will do all of the work.
Study with a singer who knows more than you do about proper singing. While the best teachers will command higher rates, anyone who knows more about the technical aspects of singing will likely be able to help you. Be sure that your teacher encourages you to perform for audiences, no matter how small, and that he or she is eager to expand your repertoire of arias.
Contact the music departments of local colleges or high schools to see if they can suggest good voice teachers. You could even ask a professor to connect you with a voice student who wants to teach and would like to make a little extra money.
Perform in the chorus of a local opera company. For example, the Taconic Opera of New York emphasizes working with amateur singers. While you don't need to have perfect technique when you're just starting, you "need to know how to support your voice," the opera's website says, because "what you hear comes straight from the singers and isn't reproduced electronically."