chaegeul ilgeul ttaeneun angyeongeul sseoyo.

때 means time or when.
So 읽을 때 means when reading or when I read.

The verb 읽다 changes to 읽을 because it is being used before the noun 때. In Korean, verbs often change into a noun-modifying form before words like 때.

So:

• 읽다 = to read
• 읽을 때 = when reading / when I read

Even though -을 often looks like a future-type ending in other contexts, here it is just the normal form used in this pattern.

The 는 is a topic marker. It gives 읽을 때 a feeling like:

• as for when I read
• when I read, ...
• in the case of reading, ...

It can also add a slight contrast, as if the speaker means:

• When I read, I wear glasses
  maybe implying but not necessarily at other times.

If you remove it and say 책을 읽을 때 안경을 써요, the sentence is still natural. It just sounds a bit more neutral.

Because there are really two verb phrases here:

• 책을 읽을 때는 = when reading a book / when I read books
• 안경을 써요 = I wear glasses

So:

• 책을 is the object of 읽다
• 안경을 is the object of 쓰다

Each verb has its own object, so both nouns can take -을.

Yes, 쓰다 can mean to write, but it also has other meanings. Korean has many verbs that change meaning depending on the object.

For example:

• 편지를 쓰다 = write a letter
• 모자를 쓰다 = wear a hat
• 안경을 쓰다 = wear glasses

So in this sentence, because the object is 안경, 쓰다 means to wear, not to write.

In Korean, different kinds of things use different wear verbs.

Some common ones are:

• 입다 for clothes
• 신다 for shoes
• 쓰다 for things worn on the head or face

That is why Korean says:

• 안경을 쓰다 = wear glasses
• 모자를 쓰다 = wear a hat

So even though English uses wear for many things, Korean splits this idea into several different verbs.

써요 is the polite -요 style, often called haeyo-che. It is very common in everyday conversation.

The dictionary form is 쓰다.
It changes like this:

• 쓰다
• stem: 쓰-
• • -어요
• contraction: 써요

So 써요 is the normal polite present form of 쓰다.

Yes. Korean often leaves out the subject when it is already clear from context.

So this sentence could mean:

• I wear glasses when I read books
• She wears glasses when she reads
• He wears glasses when reading

In many beginner examples, it is usually understood as I, but Korean does not need to say the subject if it is obvious.

Usually it sounds like a habit or a general fact.

So 책을 읽을 때는 안경을 써요 normally means something like:

• I wear glasses when I read
• Whenever I read books, I wear glasses

It does not usually sound like one specific event unless the context makes that clear.

If you wanted to talk about a specific past case, you could say:

• 책을 읽을 때는 안경을 썼어요 = I wore glasses when I was reading / when I read

읽을 is pronounced roughly like 일글.

This happens because 읽다 has the consonant cluster ㄺ, and Korean pronunciation changes when endings are added.

So although it is spelled 읽을, the actual sound is closer to:

• 일글

This is one of those common spelling-versus-pronunciation points that learners just have to get used to.

Korean does not have to mark plural as often as English does.

So:

• 책 can mean book or books
• 안경 is simply the normal Korean word for glasses

Even though English uses a plural form glasses, Korean just uses 안경 as a regular noun. You do not need to add anything special here.

The exact singular or plural meaning usually comes from context.