1 How to support the tone. This is taught a lot of different ways but basically consists of controlling the breath as it goes out and keeping the pressure down off of your vocal chords. You're going for a low even pressure that gets stronger as you go up the scale.
2 How to enunciate clearly. Remember there is no amplification at the opera.
3 How to pronounce foreign languages. Unless you are Cecilia Bartoli or work exclusively at the ENO, you will be expected to know how to pronounce Italian, German, French and maybe English. Your teacher will tell you how to pronounce the neutral vowel in French and then someone else will tell you it's not like that at all. You can also learn to speak these languages if you like, but that is easier if you have someone to talk to. [See Diction Police. See things voice teachers worry about.]
4 How to integrate your registers. You will need to be able to convince the audience that you have only one voice and not two or three as you go up and down the scale. [See Chest Voice ]
5 How to sing legato. How to sing legato while enunciating clearly. This is actually possible. [See Legato]
6 How to place your vowels. That means your pharynx is open AND your upper formant is focused all at the same time. This is a big part of the process of getting all of your voice to sound more or less the same. [See Yawn]
7 How to sing loud. They will choose the loud one. Practice the messa di voce. Then you will be able to sing both loud and soft. And in between. [See Messa di Voce. See where Christa Ludwig recommends it. See where Vesselina Kasarova recommends it.]
8 How to sing high. No high notes, no opera. Even Placido Domingo had high notes when he started out.
9 If you are a tenor, you will need to learn how to sound like one. Being a tenor is harder. This is a specialized trick that will require you to find a teacher that knows how to do it. [See Tenor Blog. See Leggiero Tenor]
10 How to sing in tune. You are allowed to sing out of tune sometimes but only on purpose. Some teachers will put this at the top of the list, but this is a mistake. If this is really hard for you, maybe you shouldn't be a classical musician. The better your breath support the easier it is to sing in tune.
11 If you want to be a coloratura, you will need to know how to sing fast and with less legato. You will need to learn how to trill. [See Vibrato/Trill and Trill]
12 How to do all of these things at the same time.
Put off classification as long as possible. And practice. It's no use knowing how to do things if you don't practice. This list is the result of listening to a lot of students. They're not really learning anything.