Я посмотрела на этикетку кроссовок и поняла, что взяла не тот размер.

Because the speaker is female.

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

• masculine: посмотрел, понял, взял
• feminine: посмотрела, поняла, взяла
• neuter: посмотрело
• plural: посмотрели

So this sentence sounds as if a woman is speaking. If a man said it, it would be:

Я посмотрел на этикетку кроссовок и понял, что взял не тот размер.

They describe completed actions or single events.

• посмотрела = took a look
• поняла = realized / came to understand
• взяла = took / picked

Perfective aspect is very natural here because the sentence tells a sequence of finished events:

1. she looked,
2. then realized,
3. that she had chosen the wrong size.

If you used imperfective forms, the meaning would shift:

• смотрела = was looking / looked repeatedly
• понимала = understood / was understanding
• брала = was taking / used to take

Those would not fit this one-time discovery as well.

Because the verb посмотреть на requires на + accusative when it means look at.

So:

• посмотреть на кого? что?
• на этикетку

This is just how the verb is built in Russian. Even though English learners often associate на with location, here it is part of the pattern for looking at something.

Compare:

• Я посмотрела на этикетку. = I looked at the label.
• Надпись была на этикетке. = The writing was on the label.

In the second example, на этикетке is location, so it uses the prepositional case.

It is accusative singular.

The dictionary form is этикетка. Since it is a feminine noun ending in -а, the accusative singular changes to -у:

• nominative: этикетка
• accusative: этикетку

It is accusative because it is the object of посмотрела на.

Кроссовок is genitive plural.

The phrase means something like the label of the sneakers. In Russian, when one noun modifies another in this of relationship, the second noun is often put in the genitive:

• этикетка чего? = label of what?
• кроссовок

So:

• этикетка кроссовок = the sneakers’ label / the label on the sneakers

The dictionary form is кроссовки. Its genitive plural is кроссовок.

Because it is actually genitive plural, even though the form may not look obviously plural to an English speaker.

The noun кроссовки is normally used in the plural, like sneakers. Its case forms include:

• nominative plural: кроссовки
• genitive plural: кроссовок

So кроссовок here still refers to the sneakers, not to one sneaker.

This kind of form is very common with Russian plural-only or usually-plural clothing items.

Что introduces the subordinate clause: that.

So the structure is:

• поняла, что... = realized that...

In English, that is often omitted:

• I realized I took the wrong size.

In Russian, что is usually kept in this kind of sentence:

• Я поняла, что взяла не тот размер.

So even if English drops that, Russian normally does not.

Because Russian often omits subject pronouns when the subject is clear from context or from the verb form.

The sentence starts with Я, so after that it is obvious that the same person is still acting:

• Я посмотрела ... и поняла, что взяла ...

Russian does not need to repeat я the way English often repeats I.

You could say:

• Я посмотрела на этикетку кроссовок и я поняла...

But that would usually sound unnecessary or emphatic.

Yes, but in shopping contexts взять often means take / choose / pick / go with / end up getting.

So взяла размер can mean:

• picked a size
• took that size
• chose that size

This is very natural in Russian when talking about buying or selecting something in a store.

Other verbs are possible, depending on nuance:

• выбрала = chose
• купила = bought
• заказала = ordered

But взяла is very idiomatic for I took/picked this one.

Тот literally means that, but in expressions like this it often means the right one / the intended one by contrast.

So:

• тот размер = the size I was supposed to take / the correct size
• не тот размер = the wrong size

This is a very common Russian pattern:

• не тот человек = not the right person
• не то место = not the right place
• не то время = not the right time

So не тот размер sounds very natural and idiomatic.

Because размер is the direct object of взяла, so it should be in the accusative. But for an inanimate masculine singular noun, the accusative looks the same as the nominative.

So:

• nominative: размер
• accusative: размер

That is why the form does not change.

Compare with an animate masculine noun:

• Я вижу брата.
  Here accusative is different from nominative because брат is animate.

But размер is inanimate, so accusative = nominative.

Yes. Russian word order is flexible, though the original order is very natural.

The given sentence presents the events in a straightforward way:

• first she looked,
• then she realized.

You could change the order for emphasis, for example:

• Я поняла, что взяла не тот размер, когда посмотрела на этикетку кроссовок.

That version puts more focus on the realization.

But the original:

• Я посмотрела на этикетку кроссовок и поняла, что взяла не тот размер.

is probably the most neutral and natural way to say it.