Hit the High Notes, Classical Style

How to hit the high notes without sounding like a cat in heat.

Steps

As always, warm up your voice with simple vocal exercises, such as humming through ascending arpeggios etcetera before you sing. Go as high up as you can for your vocal range without straining your throat.
Identify the high note you want to hit. Ensure that this note is within an achievable range. Preferably, it was the last or penultimate note you could comfortably reach during the warm-up exercises.
Sing the note an octave below it first. Next, breathe deeply into your diaphragm and back, and simultaneously drop your inner jaw and raise your soft palette without also dropping your tongue or raising your larynx. If this sounds hard to execute in a split second, it is.
Place your voice high up in your head (above your cheekbones, or even above your eyebrows). It helps to imagine that the top of your head is big and empty. Now sing the high note with gentle yet firm support from your lower body. You should have the sensation that you are hollering.
Remember that though your voice is placed in your head, it first stemmed from your diaphragm. While singing, your voice should reverberate in your head first before being projected outside of your body.
Practice singing the two notes an octave apart for many times. Move on once you manage to achieve a rich tone for your high note.

Keep your throat loose and relaxed, like a when you're yawning. If you squeeze it, it will sound more like a screech.
If your voice cracks when you hit the high notes, it is likely that you are singing from your throat, which damages your voice. Push your larynx down your throat. This action is also achieved by trying to yawn politely, sneeze, or in this case, retch.
Always always always make sure you have enough air to support your sound.
Avoid tensing up before singing the high note; this leads to the tightening of throat muscles and subsequently the cracking of the voice. Many singers tense up because they are daunted by their apparent inability to hit the high notes, even before singing it! Overcome this by believing in yourself.
To aid the dropping of the jaw and raising of the uvula, it is helpful to think that you are politely yawning, or are about to sneeze. Do not drop your jaw as you sing, but rather drop before.
Drink water. Water helps hydrate your throat.
To prevent any abrupt changes in tone, it helps to think that the two notes are lying just next to each other, rather than far apart.

Do not over strain your voice. If nothing more than a squeak is possible, stop trying and rest your voice. Over straining your voice could lead to the growth of scar tissues forming on your vocal chords, which permanently damages the quality of your voice.
If your voice goes out, and you see that you cannot hit a high note anymore relax your voice then try again later.
Always seek professional advice when in doubt.