Study opera. See as many operas as you can and develop a wide knowledge of operatic history and repertory. Although it can be expensive to see live opera, recordings of opera are cheaply and widely available.
Learn to read music. This is not easy without a teacher, but can be done with the help of music tuition books and CDs. You will need some sort of tuning equipment; a piano or keyboard is great. If you don’t have a keyboard, see if your local church has a piano you can use for free. Offer to help with flower arranging or some other chore in return. Better still, join the church choir!
Study languages. Few operas were written in English. Italian, French, and German are the usual languages used in opera.
Protect your voice. This is important. If you spend weeks and months singing challenging operatic arias without having any training, you are likely to damage your vocal cords irrevocably. If this happens, you will never make it as a singer. This is very important if you are young, as your vocal cords are still developing. Many challenging arias are not sung even by experienced operatic singers until they are over 30.
Check your local library for books on singing technique. Many of these will come with a CD, so you can hear the exercises. Be warned that a singing CD will never be able to teach you technique in the same way as a live teacher, as the CD cannot hear if you are doing something wrong. The longer you persist in doing something wrong, the more chance you have of damaging your vocal cords.
Check out Speech Level Singing. SLS technique is currently extremely popular with singers of all musical styles. SLS helps vocalists to maximize their range and depth of tone without damaging their voice. While SLS lessons can be expensive, there are resources on the web that should give you some good advice.
Join a good classical choir. While choral singing is not the same as operatic singing, a competent choir leader should know a good deal about vocal technique and will be able to advise you. You will also gain a lot of singing experience, and may be asked to sing solos. Again, take care to protect your voice and never sing so that your throat becomes sore.
Plan ahead. If you are serious about becoming an opera singer, at some stage you will need training. If this means taking two extra jobs in order to pay for lessons, then do it.