Learn Hardcore Greek: Η υπάλληλος δουλεύει στο κατάστημα σήμερα. - The employee is working at the store today.

Η is the feminine singular definite article in the nominative case. It roughly corresponds to English the, but Greek uses definite articles more often, especially with people’s professions and roles. So η υπάλληλος is literally the employee, not just employee. The gender (feminine here) is shown by the article, not by the noun ending alone.

Why is it Η υπάλληλος and not Ο υπάλληλος, since -ος nouns are usually masculine?

Υπάλληλος is a common-gender noun: its form stays the same, and the article shows whether the person is male or female.

ο υπάλληλος = the (male) employee
η υπάλληλος = the (female) employee

So the -ος ending does not automatically mean masculine; you have to look at the article.

Where is the word she in this sentence? How do I know it’s she works?

Greek usually omits subject pronouns like I, you, he, she, we because the verb ending already tells you who is doing the action, and the noun phrase makes it clear.
Here, η υπάλληλος is the subject, and it is feminine because of η, so we understand it as she. The full idea she (the employee) works at the store today is expressed without a separate word for she.

What tense is δουλεύει? Does it mean works or is working?

Δουλεύει is the present tense, 3rd person singular of δουλεύω (to work).
In Greek, the present tense usually covers both English present simple and present continuous, so it can mean:

she works (as a general fact)
she is working (right now / today)

The exact meaning comes from context, here helped by σήμερα (today).

What is the dictionary form of δουλεύει, and how do I conjugate it for other people?

The dictionary (infinitive-like) form is δουλεύω (I work). Present tense forms are:

(εγώ) δουλεύω – I work / I am working
(εσύ) δουλεύεις – you work (singular, informal)
(αυτός/αυτή/αυτό) δουλεύει – he / she / it works
(εμείς) δουλεύουμε – we work
(εσείς) δουλεύετε – you work (plural or polite)
(αυτοί/αυτές/αυτά) δουλεύουν(ε) – they work

In everyday speech the final -ε in δουλεύουνε is often dropped.

What exactly does στο mean? Is it in, at, or to?

Στο is a contraction of σε + το and means in the / at the / to the, depending on context.

σε is a preposition covering meanings like in, at, to
το is the neuter singular article the

So στο κατάστημα literally is in/at/to the store. In this sentence, the natural English is at the store.

Why is it στο κατάστημα and not just σε κατάστημα?

Greek tends to use the definite article much more than English, especially with specific places.
Σε κατάστημα would sound like in a store (non-specific), while στο κατάστημα is in/at the store (a specific store understood from context). Also, στο is the very common contracted form; saying σε το κατάστημα is grammatically possible in theory but not used in practice.

What does κατάστημα mean exactly? Is it the same as μαγαζί?

Κατάστημα means store, shop and sounds a bit more formal or neutral, often used in written language, business, or official contexts (εμπορικό κατάστημα = commercial store).
Μαγαζί also means shop / store, but is more colloquial and very common in everyday speech.
In this sentence you could also say Η υπάλληλος δουλεύει στο μαγαζί σήμερα with almost the same meaning, just a slightly more informal feel.

What gender is κατάστημα, and why does it take το?

Κατάστημα is a neuter noun. Neuter singular nouns usually take the article το in the nominative and accusative.
So:

το κατάστημα – the store (subject or object)
του καταστήματος – of the store
τα καταστήματα – the stores

In στο κατάστημα, το is still there inside στο (σε + το).

Does στο change the case of κατάστημα?

Yes. In Modern Greek, nouns after most prepositions (including σε) are in the accusative case.
Here we have σε + το κατάστημα → στο κατάστημα, with κατάστημα in the accusative. For neuter singular nouns, the nominative and accusative look the same, so you don’t see a form change, but grammatically it is accusative.

Can σήμερα go somewhere else in the sentence?

Yes, adverbs like σήμερα are quite flexible. All of these are correct, with only slight changes in emphasis:

Η υπάλληλος δουλεύει στο κατάστημα σήμερα.
Η υπάλληλος σήμερα δουλεύει στο κατάστημα.
Σήμερα η υπάλληλος δουλεύει στο κατάστημα.

Placing σήμερα at the beginning (Σήμερα...) tends to emphasize today a bit more.

Is there a more formal way to say δουλεύει here?

A more formal or “official” verb is εργάζεται (from εργάζομαι).
So you might see Η υπάλληλος εργάζεται στο κατάστημα σήμερα in more formal writing or official descriptions. Δουλεύει is perfectly normal and very common in everyday spoken Greek.