На новой блузке висела бирка, и я не заметила её сразу.

Because на here means on and is used for location. After на in the meaning of location, Russian normally uses the prepositional case.

So:

• на блузке = on the blouse
• на новой блузке = on the new blouse

If на meant movement onto something, Russian would use the accusative instead instead of the prepositional.

Both words are feminine singular and are in the prepositional case because of на.

• новая → новой
• блузка → блузке

The adjective has to agree with the noun in gender, number, and case, so both words change together.

Because the subject is бирка, and бирка is a feminine singular noun.

In the past tense, Russian verbs agree with the subject in gender and number:

• masculine: висел
• feminine: висела
• neuter: висело
• plural: висели

So бирка висела = the tag was hanging.

Russian word order is more flexible than English word order. The sentence begins with На новой блузке to set the scene first: On the new blouse...

Then comes висела бирка. This is very natural in Russian when introducing something that is present somewhere.

A more neutral English-style order, Бирка висела на новой блузке, is also possible, but it puts the focus a little differently.

Заметить is perfective, and here it means to notice as a single completed event.

So я не заметила её сразу means I didn’t notice it right away.

If you used не замечала from замечать instead, it would suggest an ongoing or repeated failure to notice, more like:

• I wasn’t noticing it
• I kept not noticing it
• I hadn’t been noticing it

For this sentence, perfective не заметила is the natural choice.

Because the speaker is female.

In Russian past tense, verbs agree with the subject in gender when the subject is singular:

• я заметил = I noticed said by a man
• я заметила = I noticed said by a woman

So this sentence tells us the speaker is female.

Because её is the object form of она.

Here, the tag is the thing being noticed, so it is a direct object:

• она = she / it as the subject
• её = her / it as the object

So:

• Она висела. = It was hanging.
• Я не заметила её. = I didn’t notice it.

Here её refers to бирка.

It means it.

Russian nouns have grammatical gender, so бирка is feminine, and the pronoun referring to it is also feminine: её. But in English, tag is usually it, not she.

So even though the Russian pronoun is grammatically feminine, the natural English translation is it.

Сразу means right away, immediately, or at once.

So:

• я не заметила её сразу = I didn’t notice it immediately
• more natural English: I didn’t notice it right away

It implies that the speaker noticed it later, but not at the first moment.

Sometimes Russian can omit an object if it is very clear from context, but here её sounds natural and helpful.

• Я не заметила её сразу = clear and complete
• Я не заметила сразу = possible in context, but less explicit

Keeping её makes it clear that what the speaker did not notice was the бирка.

Yes, висела comes from висеть, which means to hang or to be hanging.

In this sentence, it means the tag was physically attached and hanging on the blouse. English might translate this in different ways:

• A tag was hanging on the new blouse
• There was a tag on the new blouse
• A tag was attached to the new blouse

Russian uses висела because it describes the tag’s visible hanging position.

Russian does not have articles like a or the.

So бирка can mean:

• a tag
• the tag

The exact meaning depends on context. In this sentence, English often uses a tag when first mentioning it:

• There was a tag hanging on the new blouse...

Later, once it is already known, English could refer to it as the tag or it.

Yes, it sounds natural.

Russian often begins with a place or location and then says what was there:

• На стене висела картина. = A picture was hanging on the wall.
• На двери висела табличка. = A sign was hanging on the door.
• На новой блузке висела бирка. = A tag was hanging on the new blouse.

This pattern is very common when describing what is located somewhere.