The logic of sheet music
While sheet music can look obtuse and unreadable on first impression, the fundamental logic of sheet music is actually extremely simple. Possibly the best way of discovering this simplicity, is to walk through the steps of reinventing sheet music for yourself.
Lets reinvent sheet music
If you had to design a way of notating music graphically, how would you approach it? You know that melodies are a series of notes from a scale, arranged one after another in time.
You may think of a graph, where vertical position represents the note to play, with higher notes towards the top, and horizontal position represents time, increasing towards the right:

But from this alone, you may find that it is unclear which position represents which pitch. So as the next evolution, you try using some lines, and indicate which note to play by circling the line:

Yet, there are still two problems:
- It is hard to recognise which line you are on as they all look the same.
- It is not clear when each note should be played, as there is no horizontal scale.
To address this, you do a few things. First, you realise that you can show twice as much range, in half the space if you use both the lines, and the spaces between them to represent different notes.

Secondly, you decide to only show 5 of the lines, and show notes outside of this range using short 'ledger lines', indicating where the line would have been.

The 5 lines serve as 'home base', giving you a consistent visual reference, so that it remains clear where a note is regardless of how many notes are used.

And finally, you modify the shapes of the notes to indicate different time values, adding a stick to the shorter notes.

This is essentially how sheet music works. Different vertical positions represent different notes on your instrument, and the shapes of the note symbols represent how long that note will last for.
Note symbols
Notes are a collection of different symbols which sheet music uses to tell you what notes to play, and also the duration of the note.
Notes look like this, and you will have certainly seen the eighth and sixteenth note symbols before as they are frequently used to represent 'music' as a cultural idea:

The cultural use of these symbols can be a source of confusion, due to the heavy use of eighth note symbols. Whole notes for example may not look 'right' intuitively. Just stick with it, and it will make sense over time.
Notes have different parts:

- Head. All notes feature a head. A note's head circles a line, and the position of the head tells you which note to play on your instrument.
- Stem and flags. The stem and flags are features added to the circle to represent notes of different time durations. Not all notes have them.
The staff and clef
Sheet music represents notes using the staff, a set of 5 lines and 4 spaces. As was explored during the introductory section, both the lines and spaces represent different notes, and pitch increases towards the top.

At the beginning of every staff line you'll find a clef. The clef tells you which notes are on which line or space on the staff. Different clefs exist, but as a player of a melody instrument, you will be using the treble clef almost exclusively.
The treble clef looks like this:

Staff values
The treble clef states that the note G may be found on the second line of the staff. For clarity I have highlighted it below:

The position of a note's head on the staff tells you which note to play on your instrument. Circling the line G tells you to play a G on your instrument. On an ocarina in C you would use the following fingering:

Note that only the position of the head describes the pitch. Despite having different shapes, all of the following represent the same note on an instrument:

The other notes are defined relative to this point. If a note circles the space below the G line you take one step down the scale. The music now tells you to play an F.

And here are the rest of the notes of the C scale that fit within the range of an alto C ocarina. You can find out how to finger these using your instrument's fingering chart.

Note that if you see music notation that is 'polyphonic', asks you to play more than one note at once, how you handle this is play the top note as this is the melody note.
Learning which notes are where
There are a few tricks that you can use to remember where notes are on the treble clef staff:
- The notes of the spaces spell the word 'FACE', from bottom to top.
- The lines are EGBDF, which you can remember with "Every good boy deserves fudge".
- You always have the option of counting a note position up or down from the G line, or another reference note you have memorised.
To practice remembering which note is on which line:
- Get some staff paper (music notation paper)
- Ask a friend to draw notes for you.
- As notes are drawn, say the name aloud.
Starting with a small range, and then gradually adding more notes may help you at first, although it is perfectly fine to look them up, or count them up or down from the G line if you need to.
There are also apps that will generate random notes to help you learn, and a basic one is provided below:
How sheet music notates rhythm
As well as pitch, sheet music also notates rhythm, starting with the time signature. A time signature is two numbers that describe the rhythmic grouping of a piece of music.

For example the time signature '4/4' (read 'four, four') means '4 quarter notes'. These are separated by vertical lines called 'bar lines'.

Further details on how sheet music notates rhythm are covered in the article Understanding rhythm.
Sharps and flats
If you remember from Octaves and scale formation, in western music the octave is split equally into 12 semitones, named:
C, C♯, D, D♯, E, F, F♯, G, G♯, A, A♯, B
These names repeat over multiple octaves, and the 12 major scales can be formed from this using the formula:
whole, whole, half, whole, whole, whole, half
Sheet music is designed to notate a single one of these 7 note scales, as thinking about the 'gaps' would be needlessly complicated. Most music only uses 7 notes at a time.
By default, notes placed on the staff represent the 'natural' notes, the notes which are named using neither a sharp (♯) or flat (♭).

Sheet music tells you to play the in-between notes using either sharps, or flats. Adding a sharp tells you to play the note that is 1 semitone higher.

Adding a flat tells you to play the note that is 1 semitone lower:

Sharps and flats affect the pitch of the note in all octaves, and are effective until the next bar line. so repeating notes will also be sharp or flat.

To return to the natural note, a natural (♮) is used:

Key signatures
If you remember, the scale of G major contains an F sharp. You could notate music in G by adding a sharp sign before every F, but it would be cumbersome longer music.
The key signature provides a means of making certain notes sharp or flat 'by default'. A key signature is one or more sharp or flat signs that are placed after the clef at the start of the music.

The key signature for any single key always looks the same, with the sharp or flat symbols in the same order, in the same vertical positions. It makes it easier to recognise which notes are used in a piece of music, without needing to scan through the whole melody.
You can see all of the common key signatures below. The circle of fifths organises all of the scales such that C, which requires no key signature, is at the top, and the sharp keys are on the right, and the flat keys are on the left, in order of increasing numbers of sharp or flat symbols.

Reading notes from relative positions
One of the benefits of sheet music is that with a bit of practice, you can discern where the melody is going by reading the shapes formed by the notes on the page.
For example, the following shows two instances of a common pattern; play a note, play the note above, then play the starting note again. First from G, then again from high D. As you progress you will be able to play such patterns without caring about the named value of a higher note. You just ascend to the next note in the scale, then drop back down again.

This is explained in more detail in the article Getting started playing the ocarina with sheet music.