Gözlüğüm masada değil, çantada.

Because -üm is the suffix meaning my, and when a word like gözlük takes a vowel-initial suffix, the final k often softens to ğ.

So the pattern is:

gözlük + üm → gözlüğüm

This is a very common sound change in Turkish.

Turkish usually shows possession with a suffix attached to the noun.

So:

gözlüğüm = my glasses / my eyeglasses

You do not need a separate word like my in English. If you want extra emphasis, you can add benim:

Benim gözlüğüm = my glasses with stronger emphasis

But in normal speech, gözlüğüm by itself is enough.

The ending -da / -de / -ta / -te is the locative suffix. It usually means in, on, at depending on the noun and context.

So:

masa + da → masada = on the table / at the table
çanta + da → çantada = in the bag

Turkish uses the same case ending where English uses different prepositions.

That is because of two rules:

1. Vowel harmony
   After back vowels like a, the suffix is -da or -ta.

2. Consonant harmony
   If the word ends in a voiced sound, Turkish uses d.
   If it ends in a voiceless consonant, Turkish uses t.

So:

• masa ends in a vowel and has back vowels → masada
• çanta also ends in a vowel and has back vowels → çantada

If the word ended differently, you might get -te or -ta instead.

Because this sentence is not using an action verb like go, eat, or see. It is a location/copula sentence: something is somewhere.

In Turkish, these are often negated with değil.

So:

masada değil = is not on the table

You do not attach a negative suffix to masa. You use the separate word değil.

In present-tense Turkish, the verb to be is often left unspoken in simple sentences like this.

So:

Gözlüğüm çantada literally looks like My glasses in the bag, but it naturally means My glasses are in the bag.

This is completely normal Turkish.
When you negate that kind of sentence, you use değil:

Gözlüğüm masada değil = My glasses are not on the table

Because the second half leaves out words that are already understood.

Gözlüğüm masada değil, çantada.

This is short for something like:

Gözlüğüm masada değil, çantada.
= My glasses are not on the table, they are in the bag.

Turkish often avoids repeating material when the meaning is clear.

The locative suffix itself is broad. It can correspond to in, on, or at in English.

So the exact English preposition depends on the noun:

• masada is usually on the table or sometimes at the table
• çantada is usually in the bag

Turkish does not force the same distinction English does here.

In Turkish, gözlük is normally singular when talking about a pair of eyeglasses.

So:

gözlüğüm = my glasses

That is perfectly natural Turkish.
If you mean more than one pair, then you can make it plural:

gözlüklerim = my glasses / my pairs of glasses

Yes, you can.

That version is grammatical, but benim adds emphasis. It can sound like:

My glasses are not on the table, they’re in the bag.

Without benim, the sentence is more neutral and natural in many everyday situations:

Gözlüğüm masada değil, çantada.

The ğ in Turkish is usually very soft. It is not pronounced like a strong English g.

In gözlüğüm, it mainly smooths or lengthens the sound between vowels rather than making a hard consonant sound. For a learner, a rough guide is:

göz-lü-üm
with a very soft transition in the middle

The important thing is: do not pronounce it like a strong g in go.

Yes. Turkish word order is flexible, and changing it changes the emphasis.

The given sentence:

Gözlüğüm masada değil, çantada.

puts the contrast on not on the table, but in the bag.

You could also say:

Gözlüğüm çantada, masada değil.

That version is also natural, but it foregrounds çantada first.