Она быстро обернулась, подмигнула мне и помахала рукой.

Because the subject is она (she), and these are all past tense feminine singular forms.

In Russian past tense, the verb agrees with the subject in gender and number:

• он → usually -л
• она → usually -ла
• оно → usually -ло
• они → usually -ли

So:

• она обернулась
• она подмигнула
• она помахала

If the subject were он, the sentence would be:

• Он быстро обернулся, подмигнул мне и помахал рукой.

The ending -ся (or -сь) makes the verb reflexive.

Here, обернуться means something like to turn around or to turn back. The reflexive ending often shows that the action is directed back toward the subject or is an intransitive/self-contained action.

Compare:

• обернуть = to turn something around
• обернуться = to turn around oneself

So in this sentence:

• Она быстро обернулась = She quickly turned around

The form -сь is just a spelling/pronunciation variant of -ся used after certain endings. Learners often just memorize the verb as обернуться.

Because подмигнуть takes the person receiving the wink in the dative case.

So:

• я = I
• меня = me (often accusative/genitive)
• мне = to me

Russian treats this more like wink to someone than simply wink someone.

Examples:

• Она подмигнула мне. = She winked at me.
• Я подмигнул ему. = I winked at him.
• Они подмигнули нам. = They winked at us.

So мне is required by the verb.

Because рукой is the instrumental case of рука (hand), and here it expresses the means/instrument used to do the action.

Literally, it is like:

• She waved with her hand

In English, we usually just say waved her hand or simply waved, but Russian commonly uses the instrumental here:

• махать рукой = to wave one’s hand / to wave

Forms:

• рука = hand
• рукой = with a hand / by hand

This is a very common pattern in Russian when indicating what body part or tool is used:

• кивнуть головой = to nod one’s head
• пожать плечами = to shrug one’s shoulders
• махнуть рукой = to wave one’s hand

Russian often does not use a possessive like her, his, my when it is already obvious whose body part is meant.

So помахала рукой naturally means:

• she waved her hand
• or more naturally in English, just she waved

Russian prefers the simpler form unless the possessor needs emphasis or contrast.

So:

• Она помахала рукой. = She waved her hand / She waved.
• Она помахала своей рукой. would sound marked or emphatic, as if contrasting with someone else’s hand.

These are perfective past tense verbs:

• обернулась ← обернуться
• подмигнула ← подмигнуть
• помахала ← помахать

Perfective verbs present the actions as completed single events.

That fits the sentence well, because it describes a short sequence of finished actions:

1. she turned around,
2. winked at me,
3. waved.

If you used imperfective forms, the meaning would change and might sound like ongoing, repeated, or background action.

For example:

• оборачивалась = was turning around / used to turn around
• подмигивала = was winking / used to wink repeatedly
• махала рукой = was waving / waved repeatedly or for some duration

So the perfective forms here help create a quick, cinematic sequence.

Yes, Russian word order is flexible, and быстро can move around, but the neutral order here is very natural:

• Она быстро обернулась...

This simply means She quickly turned around...

Other orders are possible, for example:

• Она обернулась быстро...
• Быстро она обернулась...

But they can sound more marked, depending on context and emphasis.

In this sentence, placing быстро before the verb gives a smooth, neutral narrative flow.

Russian often lists several actions done by the same subject in a row without repeating the subject.

So:

• Она быстро обернулась, подмигнула мне и помахала рукой.

means:

• She quickly turned around, winked at me, and waved her hand.

The commas separate the actions in a series, just like in English. Russian does not need to repeat она before each verb because it is understood that all three actions belong to the same person.

You could repeat it, but it would usually sound unnecessary:

• Она быстро обернулась, она подмигнула мне и она помахала рукой.

That sounds heavy and unnatural in normal narration.

Подмигнуть specifically means to wink at someone.

Мигнуть more generally means to blink, to flash, or sometimes to give a quick signal, depending on context.

So:

• подмигнула мне = winked at me
• мигнула would not be the normal choice here if the meaning is a deliberate wink

The prefix под- in подмигнуть helps form this specific meaning of giving someone a wink.

Yes. In natural English, you would often simply translate it as waved.

So the whole sentence can be translated naturally as:

• She quickly turned around, winked at me, and waved.

Even though Russian explicitly says рукой (with her hand), English often leaves that out because it is obvious.

This is a good example of how a translation can be natural without matching every word exactly.

A few points may help:

• она́
• бы́стро
• оберну́лась
• подмигну́ла
• мне
• помаха́ла
• руко́й

A common learner issue is remembering that the stress is not always where an English speaker might guess. Also, the ending -сь in обернулась is pronounced lightly.

If you say the sentence smoothly, the rhythm is something like:

• Она́ бы́стро оберну́лась, подмигну́ла мне и помаха́ла руко́й.

Practicing it as one chunk is useful, because it is a very natural narrative sentence.