Reading sheet music with a key signature
By default, sheet music is designed to notate the 7 natural notes, called:
A, B, C, D, E, F, G
But in western music, we actually have octaves that are split into 12 notes, and thus there are 5 notes 'missing'.
Sheet music was designed in this way as most music only uses 7 distinct notes at a time, and thinking about the 'gaps' would be cumbersome.
If you have read Octaves and scale formation, you will know that there are 12 different scales. In order to notate these in sheet music, we change the scale of the entire staff using something called a key signature.
But before talking about key signatures, lets have a refresher on sharps and flats:
Sharps and flats
Take a look at your ocarina's fingering chart, and what you'll probably see is something like this. Notice how between C and D is a note called 'C# / Db'?

This is an in-between note, and due to a naming convention, these notes have two different names, one in relation to the note below, and one in relation to the note above.
Naming the notes in this way allows us to notate other scales, using one distinct letter per note. For example D major:
D, E, F#, G, A, B, C#, D
A sharp sign simply means to play the note that is 1 semitone higher within the chromatic scale.

Likewise, a flat sign is just the opposite, and tells you to play the note that is 1 semitone lower within the chromatic scale.

You can find the best fingerings for these in your instrument's fingering chart, as the fingerings for sharp / flat notes do vary between ocarinas.
I recommend learning to play the chromatic scale on your ocarina as it will teach you to move through the 'natural' and sharp/flat notes seamlessly.
Key signatures
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 each line of music. For example, here is the key signature for G:

The key signature affects the sharpened note in all octaves, so while only the top line F has been sharpened, the F in the bottom space is also to be played sharp.
How to play music with a key signature
Playing sheet music with a key signature on the ocarina is the same as reading sheet music without one. You just need to remember to substitute the natural note with the sharp or flat one.
This is where practising the scale, and the intervals and arpeggios within it becomes very advantageous as it teaches you how to move between the notes without needing to consciously think about the sharp / flat notes.
So:
- Practice fingerings and breath pressures for the scale, and the intervals within that scale.
- Associate the visual of the key signature with that set of fingerings.
- Practice playing some music in that key signature, possibly starting with music in a narrow range.
Scales and intervals are not there to torture instrument learner's, but to teach you how to move between the notes on your instrument effectively. Once you can do so, reading sheet music is much easier.
The common key signatures
You can see all of the common key signatures below, organised into increasing number of sharps and flats. 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. This is called the circle of fifths.
These may seem like a lot, but you don't need to learn all of them at once, rather look at which ones are commonly used in the music you want to play, and learn those first.

Key signatures are standardised, and the sharp or flat symbols for a given key are always placed in the same position. As such it makes it easier to recognise which notes are used in a piece of music, without needing to scan through the whole melody.
The order of sharps:

The order of flats:

Learning the key signatures
To practice and memorise the key signatures, start with a small selection of key signatures, and then have someone question you randomly. Once you know those, increase the set size.
There are mobile apps that will do that for you.