Learn Hardcore Greek: Μιλάω με τη μαμά μου στο τηλέφωνο.

μιλάω ends in -ω, which clearly marks 1st person singular (I) in the present tense.
So μιλάω by itself already means I speak / I am speaking.

You use εγώ only when you want to emphasize the subject, for example:

Εγώ μιλάω με τη μαμά μου, όχι ο αδερφός μου.
I am talking to my mom, not my brother.

In neutral, everyday speech, Μιλάω με τη μαμά μου στο τηλέφωνο is perfectly normal and more natural than adding εγώ.

What is the difference between μιλάω and μιλώ? Are both correct?

Yes, both μιλάω and μιλώ are correct forms of the same verb (μιλάω / μιλώ = to speak, to talk).

μιλάω is the full / colloquial form, very common in modern spoken Greek.
μιλώ is the shorter / more formal or written form.

They mean the same thing:

Μιλάω με τη μαμά μου στο τηλέφωνο.
Μιλώ με τη μαμά μου στο τηλέφωνο.

Both are grammatical; in everyday conversation you will hear μιλάω more often.

Why is it τη μαμά μου and not η μαμά μου after με?

This is about grammatical case. Greek marks the function of nouns (subject, object, etc.) with cases.

η μαμά = the mom (nominative, used for the subject)
τη μαμά = the mom (accusative, used for the object)

In the sentence:

The subject is (εγώ), understood from the verb μιλάω.
The phrase με τη μαμά μου is an object phrase with the preposition με.

Prepositions in Greek (like με, σε, για, etc.) are normally followed by the accusative case. That is why it must be:

με τη μαμά μου (with my mom)
not
με η μαμά μου (incorrect).

Why do we say τη μαμά μου with a definite article? In English we just say my mom, not the my mom.

Greek uses the definite article (ο, η, το, τον, τη(ν) etc.) much more often than English, especially with:

family members
proper names
possessed nouns in general

So:

η μαμά μου = the mom my (literally) but it means my mom
ο πατέρας μου = my dad
η αδερφή μου = my sister

In Greek, it sounds incomplete or wrong to say μαμά μου without the article in this kind of context. You normally say:

Μιλάω με τη μαμά μου.
not
Μιλάω με μαμά μου. (unnatural as a standard sentence)

Why does the article appear as τη and not την before μαμά?

The full feminine accusative article is την, but in modern Greek the final -ν is often dropped in speech and writing when the next word starts with a consonant that is easy to pronounce without it.

Basic rule in everyday Modern Greek:

την → τη before most consonants
την is usually kept before vowels and the consonants κ, π, τ, ξ, ψ, μπ, ντ, γκ, τσ, τζ for clarity of pronunciation.

Since μαμά starts with μ, which is not one of those special consonants, it is very common to say and write:

τη μαμά μου

You might still see την μαμά μου in more careful or old-fashioned writing, but τη μαμά μου is standard in modern everyday usage.

Why is the possessive μου placed after μαμά instead of before it, like in English?

In Greek, weak possessive pronouns (my, your, his, etc. as short forms) usually come after the noun:

η μαμά μου = my mom
ο φίλος σου = your friend
το σπίτι μας = our house

So the natural order is:

article + noun + possessive pronoun
→ η μαμά μου

You cannot say η μου μαμά in modern standard Greek; that word order sounds wrong.

Stronger, stressed forms of possessives (like δικός μου) behave differently, but that’s another topic. In this sentence, μου is the normal, weak possessive and must follow the noun.

What case is τη μαμά μου in, and what is its function in the sentence?

τη μαμά μου is in the accusative case (feminine singular).

Formation:

Nominative: η μαμά
Accusative: τη(ν) μαμά
Add possessive: τη μαμά μου

Function:

It is the object of the preposition με (με = with).
Together, με τη μαμά μου forms a prepositional phrase that tells us with whom the speaking happens.

So τη μαμά μου is the accusative object governed by με.

Does με here mean with or to? In English we say talk to my mom, not talk with my mom.

Literally, με means with. So με τη μαμά μου is literally with my mom.

However, with verbs of communication like μιλάω, με is the normal preposition in Greek, even if English would say talk to:

Μιλάω με τη μαμά μου.
I am talking with / to my mom.
Μιλάω με τον δάσκαλό μου.
I am speaking to my teacher.

So although the literal translation is with my mom, the natural English equivalent is to my mom, and both ideas (with / to) feel acceptable. The important takeaway: with μιλάω, you normally use με plus accusative.

What exactly is στο τηλέφωνο? How does it end up meaning on the phone?

στο is a contraction:

σε (in, at, on) + το (the, neuter singular)
→ στο = in/at/on the

So:

στο τηλέφωνο = σε το τηλέφωνο → on the telephone / on the phone

This is an idiomatic phrase in Greek meaning on the phone, by telephone. You can think of it as a fixed expression:

Μιλάω στο τηλέφωνο.
I am talking on the phone.

Grammatically:

στο τηλέφωνο is a prepositional phrase (place / medium) telling you how / where the communication happens.

Can I change the word order, for example to Μιλάω στο τηλέφωνο με τη μαμά μου? Does it sound different?

Yes, that is perfectly correct:

Μιλάω με τη μαμά μου στο τηλέφωνο.
Μιλάω στο τηλέφωνο με τη μαμά μου.

Both are natural and mean the same in context.

Nuance (very slight and often not important):

με τη μαμά μου first: you might feel a tiny emphasis on with whom you are speaking.
στο τηλέφωνο first: a tiny emphasis on the medium (on the phone).

In everyday speech, both orders are common; choose whichever feels more natural to you.

How do you pronounce the sentence correctly, especially the stress?

Syllable breakdown with stress marked (capital letters show stressed syllables):

Μι-ΛΑ-ω (mi-LÁ-o)
με (me)
τη (ti)
μα-ΜΑ (ma-MÁ)
μου (mu)
στο (sto)
τη-ΛΕ-φο-νο (ti-LÉ-fo-no)

Full sentence (phonetic-style, approximate for English speakers):

Mi-LÁ-o me ti ma-MÁ mu sto ti-LÉ-fo-no.

Key points:

The -ω in μιλάω is like o in go, but shorter.
η / ι / υ / ει / οι are all pronounced like ee in see; so μι, τη, τηλέ all have an ee sound.
Stress is important in Greek; moving it can change meaning or make words sound odd, so keep it on μιΛΑω, μαΜΑ, τηΛΕφωνο.