Σήμερα σκουπίζω το πάτωμα με τη σκούπα στο σαλόνι.

Greek is a “pro-drop” language: subject pronouns (like εγώ = I) are usually left out when the verb ending already shows the person.
The ending -ω in σκουπίζω tells you it’s 1st person singular → I sweep / I am sweeping.
If you really want to emphasize I, you can say: Εγώ σήμερα σκουπίζω το πάτωμα…, but it’s not necessary.

In Greek, the simple present (σκουπίζω) usually covers both English meanings:

• I sweep the floor every day. → Σκουπίζω το πάτωμα κάθε μέρα.
• I am sweeping the floor now. → Τώρα σκουπίζω το πάτωμα.

In your sentence, Σήμερα σκουπίζω το πάτωμα…, the word σήμερα (today) and the context tell us it’s more like “I am sweeping today / right now”, but the verb form itself is the same.

Yes, σήμερα (today) can move around; Greek word order is fairly flexible. All of these are correct:

• Σήμερα σκουπίζω το πάτωμα… (common; emphasis on today)
• Σκουπίζω σήμερα το πάτωμα… (slight focus on the action, then add today)
• Σκουπίζω το πάτωμα σήμερα… (neutral, like “I’m sweeping the floor today”)

Changing the position mainly changes emphasis, not basic meaning.

Το is the definite article (the) for neuter nouns in the singular (nominative/accusative).
Greek uses articles more often than English. Here, το πάτωμα means “the floor”, referring to a specific, known floor (e.g. in your house).

You might see πάτωμα without an article:

• in very general statements, or
• in certain phrases (titles, labels, etc.),

but in normal sentences about a specific object you almost always use the article.

Η σκούπα is nominative (subject form): the broom as a subject.
In this sentence the broom is not the subject; it’s part of a prepositional phrase: με τη σκούπα = with the broom, so the noun is in the accusative case:

• Nominative: η σκούπα (subject)
• Accusative: τη(ν) σκούπα (object / after prepositions)

So τη is the accusative form of the feminine singular article.

In modern Greek, the final ν in την / έναν is often dropped in writing unless the next word starts with:

• a vowel, or
• certain consonants: κ, π, τ, ξ, ψ, μπ, ντ, γκ, τσ, τζ.

Since σκούπα starts with σ, which is not in that group, the usual written form is τη σκούπα.
You will hear people pronounce a ν in speech quite often, but standard modern spelling is τη σκούπα here.

Με is the basic preposition meaning “with” and often marks the instrument:

• με τη σκούπα = with the broom (using the broom)

It can also mean “with” = “together with” (company):

• Με τον φίλο μου = with my friend

So yes, its core meaning is with, either in the sense of together with or by means of.

Στο is a contraction of σε + το:

• σε = in / at / to (generic preposition of place)
• το = the (neuter singular article)

So:

• σε το σαλόνι → στο σαλόνι = in the living room

Similarly:

• σε + τον → στον (e.g. στον κήπο = in the garden)
• σε + την → στη(ν) (e.g. στη δουλειά = at work)

Using στο σαλόνι implies a specific living room that speaker and listener can identify (your living room, the one in this house, etc.).
Σε σαλόνι (without article) would sound like “in a living room (somewhere, unspecific)”, which is unusual in everyday speech unless you really want to be vague or general.

Greek almost always uses the definite article for familiar, concrete, real-world places and objects like το σπίτι, το σαλόνι, την κουζίνα etc.

From the articles:

• το πάτωμα → neuter (article το)
• τη σκούπα → feminine (article η / τη)
• στο σαλόνι → το σαλόνι, also neuter (article το hidden inside στο)

In Greek, articles reliably show gender:

• ο (τον) → masculine
• η (την / τη) → feminine
• το → neuter

You learn the gender with the noun, usually by memorizing it as ο/η/το + noun.

The ending -ω on σκουπίζω marks 1st person singular, present tense, active voice:

• σκουπίζω = I sweep / I am sweeping

The full present tense of σκουπίζω is:

• εγώ σκουπίζω – I sweep
• εσύ σκουπίζεις – you sweep (singular)
• αυτός/αυτή/αυτό σκουπίζει – he/she/it sweeps
• εμείς σκουπίζουμε – we sweep
• εσείς σκουπίζετε – you sweep (plural / formal)
• αυτοί/αυτές/αυτά σκουπίζουν(ε) – they sweep

You can usually drop the pronouns because the endings already show the person.

Word order in Greek is flexible, especially for things like time, place, and manner phrases. These are all grammatical:

• Σήμερα σκουπίζω το πάτωμα με τη σκούπα στο σαλόνι.
• Σήμερα σκουπίζω το πάτωμα στο σαλόνι με τη σκούπα.
• Σήμερα, στο σαλόνι, σκουπίζω το πάτωμα με τη σκούπα.

The basic pattern (Verb + object, extra phrases around it) stays, but you can shift phrases to change emphasis or rhythm, not the core meaning.

Yes, they describe different kinds of cleaning:

• σκουπίζω = to sweep (usually with a broom; removing dust, crumbs, etc.)
• σφουγγαρίζω = to mop (with a wet mop on the floor)
• καθαρίζω = to clean (general verb, any type of cleaning)

So in Σήμερα σκουπίζω το πάτωμα με τη σκούπα, you are specifically sweeping the floor with a broom, not mopping it.