This page includes some tips that helped me with my music classes and things that have helped students I've tutored. I'll keep adding to this list as I have time.
Sight singing is so important. It can be very difficult to practice and very frustrating when you are first beginning. Here are some suggestions:
Solfege ( do, re, mi....)may take some time to master, but it gives you a very firm foundation. The syllables give you something to help associate the scale tone with and (if practiced consistently) will make you a much better sight reader.
I suggest that you practice saying the syllables in rhythm before attempting to sing the pitches. Pick a tempo slow enough that you can say them steadily without halting and read through the piece or exercise saying them in a monotone voice, but keeping with the right rhythm. This will help train your mind to think of the syllable for each scale degree immediately. Once you get to the point that you can easily think of the syllables, start singing the pitches.
Singing scales in solfege and trying to hear them clearly in your mind can also help your sight singing. You may want to softly hum a pitch occasionally to help your imagination hear it in your head. Once scales become easy, move on to singing up and down by in thirds. (do, mi, re, fa, mi, so etc...). Hum as necessary, but make a conscious effort to hear it in your head.
Melodic ear-Trainingestablish a key by playing a I IV V I progression. Sing do and then check yourself on the piano. Then sing a different syllable and check yourself. At first you will want to come back to do after every other pitch, but gradual increase the number of pitches you sing before playing tonic (do). This will help develop your ability to remember where tonic is.
There are two basic steps in ear-training. The first is to get the melody into your head where you can remember it. The second is to figure out what pitches are being played and write them down.
It is helpful to start practicing on the second step of the process first. By practicing writing down melodies that you already know, you can leave out the step of learning a new melody. Choose a piece that you can easily and accurately hum the melody, but one that you aren't used to playing on your instrument. Hymns, Christmas Carols, fold songs and some praise and worship choruses are good choices. You can use pop or classical melodies, but sometimes they can be pretty complicated. Pop uses a lot of syncopation so the rhythm can be difficult to notate. Classical music can change keys often. You will want to use a pieces that are hard enough that they will stretch your ability (at first this will be almost anything), but easy enough that you won't get discouraged.
Once your chosen the piece you want to notate sing it through in your head and try to find its form. You may discover that it is just two sections that repeat or two sections that repeat using different endings. Write the form at the top of your piece of staff paper.
Now you're ready to actually start notating the piece. This should be done in your head and using your voice. Do not use an instrument to figure it out. If you must, write a few bars and then check them on your instrument, then put the instrument down and continue. If you've made any mistakes fix them using only your head and your voice to find the correct pitches.
Determine the pieces time signature and write it down. Remember that some pieces can be notated in more than one time signature so find one that makes logical sense to you.
The next step is to determine what pitch is do in the piece. It will be the pitch that feels most at rest--usually the starting and ending pitches are do. Some people try to notate pieces by finding the interval between each individual pitch. This can be dangerous because if you get off with just one interval it will throw all the other notes off. I recommend relating each pitch to tonic (do). That way if you get one note wrong it doesn't mess up the rest of your transcription.
Start writing the pitches and rhythms. If the rhythms are tricky it some times helps to tap them out and write them above the correct bars. Then go back and figure out what the pitches are.
As you transcribe keep going back and sight-singing through it to check for errors. Make sure you try to sing what you've written and not just they way you remember the song goes.
This often can be the most difficult part of ear-training tests. Usually you are limited in the number of times you get to hear the piece so it is important to grasp it quickly.
Probably the most helpful things in remembering a melody is to try to grasp its form or structure. If you know that it is 8 bars long and made up of two 4 measure phrases, you have a "container" to help your memory sort out the melody. If you also know that the beginning of both phrases are the same, you'll have an even easier time remembering the melody.
When taking tests you should mark out the measures first (hopefully your teacher will tell you how many measures long it is) and then scan through the measures on your first listening marking places that are similiar or the same. Marking where the phrases start and end also helps.
The most important thing in understanding a piece is to try to understand the overall structure first instead of trying to memorize each individual note. In someways it is similiar to the way we identify people approaching us. The first thing we notice is that they are a person. As we get closer we can tell if they are a male or female and as they get even closer than that we can discover what shape their nose is, what color their eyes are, and other smaller details. On the other hand if you were to try to identify the eye color of someone approaching before you could even tell if they were male or female, you would confuse yourself and probably end up missing very important details that you could see at the time. For example you might miss the color of their hair because you are trying to see their eyes.