The first step in learning to sight-sing is to be able to reliably sing a note, which means to reproduce with your voice a pitch you hear with your ears:
This ability is needed in any singing of course; a person who cannot reproduce a given note is not able to sing in tune and is often called "tone-deaf".
Everyone can improve this ability with practice, but (in my experience) there are a small number of people who never master this first step.
The learning of this skill involves training the brain, not the ears or voice.
To be able to sight-sing to any moderate level, you need to be able to reliably reproduce a note almost automatically, so this needs to be practised until it becomes so.
Exercise (please read the comments on how to do these exercises, and what is needed):
Click on the relevant "Notes1" link, depending on whether you have a high or low voice;
In each file there are 12 notes sounded, and each note is played twice:
first long for you to sing with;
then short for you to check your pitch again.
Sing the note you hear, as soon as possible after you hear it. Sing out loud, to "Ah" or "Laa" with an open mouth and try to feel how you adjust the note to what you hear.
Keep a steady note going in one breath until after the note finishes, then check that the repeated note sounds the same as the note you sung, then take a breath ready for the next one.
You are aiming to reproduce the note as soon after you hear it as possible, but take your time at first to make sure you get it right. Later, it is a good idea to keep singing the note until the repeated tone.
If you are still unsure what to do, listen to this demonstration of me singing the first few notes of Notes2 (only do this if you are desperate!), and try singing it with me (this is a wav file, nearly 200Kb in size, so could take a few seconds to download).
When you are confident that you are doing the whole of "Notes1" correctly, go on to "Notes2", and so on. They get faster as you go down, so sing each note for a shorter time, but you have to sing each note more quickly.
There are other ways to practise this skill apart from sitting at your computer and singing to it! In order to reproduce a note, you simply need to be able to hear a reliable note:
Use a musical instrument you have access to:
A piano or electronic keyboard is best, but almost any musical instrument that produces a decent note will do.
A drum or cymbal is no good, and don't use a toy xylophone or something else that's very "tinny" - the pitch may not be very clear.
Play notes at random (you should soon find out which are too high or low for you to sing) and practise singing the note as soon as possible after you hear it, then play the same note again to check:
Or use another person! Ask someone else to sing a note at random, and you have to copy it as soon as possible.
Other (non-musical) instruments that you might find around the home can also be used. A good quality vase (glass or crystal) often gives a good note when "pinged" (I am not responsible for breakages!). Anything with a motor (razor, vacuum etc.) also normally produces a reasonably clear note, if you listen for it.
Use music you hear around you in everyday life - on the radio, on a CD or tape, in the elevator/lift etc.
A lot of people can sing-along with a tune they hear on the radio, but don't think about whether they are doing it correctly or not.
If you get into the habit of singing or humming any note you hear, whether it is from a passing train whistle or the fan in your PC, you will soon find you can reproduce any note almost automatically.
Once you have mastered reproducing a note, you can move on to more advanced voice and ear skills which are very useful for sight-singing:
The ability to remember a note in your head without singing it and then sing it several seconds later - see Remember and reproduce a note.
