Moja ciocia była kiedyś sprzedawczynią, a dziś jest kierowniczką małego sklepu.

Because ciocia is a feminine noun, so the possessive adjective must also be feminine.

• mój = my for a masculine noun
• moja = my for a feminine noun
• moje = my for a neuter noun

So:

• moja ciocia = my aunt
• compare: mój wujek = my uncle

Była is the past tense feminine singular form of być (to be).

Because ciocia is feminine, the verb in the past tense must match it:

• był = he was / it was masculine
• była = she was / it was feminine
• było = it was neuter

So:

• Moja ciocia była... = My aunt was...

This is one of the big differences from English: in Polish, past tense verbs agree with gender.

Here kiedyś means once, formerly, or at one time in the past.

So była kiedyś sprzedawczynią means something like:

• she used to be a saleswoman
• she was once a saleswoman

A useful note: kiedyś can also mean sometime in other contexts, including future ones, but with a past-tense verb like była, it clearly points to the past.

Because after być in this kind of sentence, Polish very often uses the instrumental case for professions, roles, and identities.

The dictionary form is:

• sprzedawczyni = saleswoman / shop assistant

But in the sentence it becomes instrumental singular:

• sprzedawczynią

So:

• ona była sprzedawczynią = she was a saleswoman

This is very common:

• jest nauczycielką = she is a teacher
• był lekarzem = he was a doctor

For the same reason as sprzedawczynią: after jest (is), a profession or role is commonly put in the instrumental case.

• dictionary form: kierowniczka = female manager
• instrumental form: kierowniczką

So:

• jest kierowniczką = she is a manager

This pattern is extremely important in Polish:

• Jestem studentem = I am a student
• Ona jest lekarką = She is a doctor
• On jest inżynierem = He is an engineer

These are instrumental singular endings for feminine nouns.

• sprzedawczyni → sprzedawczynią
• kierowniczka → kierowniczką

A simple way to think of it:

• many feminine nouns ending in -a take -ą in the instrumental
• some feminine nouns ending in -i / -yni change to -ią

So:

• nauczycielka → nauczycielką
• artystka → artystką
• sprzedawczyni → sprzedawczynią

You do not need to memorize a rule for every noun immediately, but it is good to notice these patterns.

Because kierowniczka here means manager of something, and after that Polish uses the genitive case.

You can think of it as:

• kierowniczka czego? = manager of what?
• answer: sklepu = of a shop/store

So:

• sklep = shop/store
• sklepu = of a shop/store

The adjective must match too:

• mały sklep = a small shop
• małego sklepu = of a small shop

So the whole phrase means:

• kierowniczką małego sklepu = manager of a small shop

In this sentence, a links two clauses with a slight sense of contrast or change:

• była kiedyś sprzedawczynią, a dziś jest kierowniczką...
• she used to be a saleswoman, and/but now she is a manager...

So a here is not just a plain and. It is closer to:

• and now
• whereas
• but

If you used i, it would sound more like simple addition, with less contrast.

Yes, in most situations dziś and dzisiaj both mean today.

• dziś is a bit shorter and often feels slightly more compact or literary
• dzisiaj is very common in everyday speech too

In this sentence, either would work:

• a dziś jest...
• a dzisiaj jest...

Both are natural.

Because Polish normally uses a comma before a when it joins two clauses.

Here you have:

• Moja ciocia była kiedyś sprzedawczynią
• a dziś jest kierowniczką małego sklepu

So the comma separates the two parts of the sentence.

This is standard Polish punctuation.

Its basic meaning is aunt, but it is also a warm, familiar word, closer in feeling to auntie than to a very formal aunt.

It can also sometimes be used by children, or as a friendly way to refer to an older woman known to the family, depending on context.

In this sentence, though, the normal meaning is simply my aunt.

They are feminine forms.

• sprzedawca = salesman / shop assistant

• sprzedawczyni = saleswoman / female shop assistant

• kierownik = manager, male manager
• kierowniczka = female manager

Polish often marks the gender of professions more clearly than English does.

In your sentence, both job titles are feminine because they refer to ciocia.

Yes. Polish word order is more flexible than English word order, because endings carry a lot of grammatical information.

For example, these are possible:

• Moja ciocia była kiedyś sprzedawczynią, a dziś jest kierowniczką małego sklepu.
• Kiedyś moja ciocia była sprzedawczynią, a dziś jest kierowniczką małego sklepu.
• Dziś moja ciocia jest kierowniczką małego sklepu, a kiedyś była sprzedawczynią.

The basic meaning stays the same, but the emphasis shifts slightly.

A rough English-friendly guide:

• moja ≈ MO-ya
• ciocia ≈ CHO-cha
• była ≈ BIH-wa or BUH-wa depending on how closely you imitate Polish y
• kiedyś ≈ KYEN-dyesh
• sprzedawczynią ≈ spshe-dav-CHI-nyon
• dziś ≈ jeesh
• jest ≈ yest
• kierowniczką ≈ kye-rov-NICH-kon
• małego ≈ ma-WEH-go
• sklepu ≈ SKLE-pu

A few key sounds:

• ci before a vowel often sounds like soft ch
• dziś has a very soft initial sound, a bit like j
• ą at the end is a nasal vowel, often approximated by English speakers as on or om, though the real Polish sound is different

If you want, I can also break the whole sentence down syllable by syllable.