Χαμογελάω στη φίλη μου όταν τη βλέπω στο πανεπιστήμιο.

Because χαμογελάω means to smile at someone in Greek, so the person is introduced with σε.

• σε + τη φίλη μου → στη φίλη μου
• literally: to my friend

So in this sentence, η φίλη μου is not the direct object of χαμογελάω. It works with σε, just like English smile at someone.

στη is the contraction of σε τη.

This is very common in Greek:

• σε + τη → στη
• σε + το → στο
• σε + τον → στον

So:

• στη φίλη μου = to/at my friend
• στο πανεπιστήμιο = at/to the university

These contracted forms are the normal ones in everyday Greek.

In Greek, possessive words like μου, σου, του, της usually come after the noun.

So:

• η φίλη μου = my friend
• το σπίτι μου = my house
• ο αδερφός της = her brother

That is the normal Greek pattern.
Literally, η φίλη μου is closer to the friend of me, but in natural English it means my friend.

τη is the weak object pronoun meaning her.

So:

• βλέπω τη φίλη μου = I see my friend
• τη βλέπω = I see her

In the sentence:

• όταν τη βλέπω = when I see her

The pronoun is used to refer back to τη φίλη μου. Greek often uses these short object pronouns before the verb.

Both are related to the same pronoun: την = her / the in the feminine accusative.

In actual speech and writing, the final -ν is sometimes kept and sometimes dropped, depending on pronunciation and the following sound.

Before some consonants, you will often see and hear:

• τη βλέπω

You may also encounter:

• την βλέπω

Both are understandable, but τη βλέπω is very common in modern usage.

Because the two parts do different jobs:

• στη φίλη μου tells you who I smile at
• τη in τη βλέπω means her, the object of see

This is not unnecessary repetition. The sentence structure is:

• Χαμογελάω στη φίλη μου = I smile at my friend
• όταν τη βλέπω = when I see her

English also does something similar:

• I smile at my friend when I see her.

όταν means when.

It introduces a time clause:

• όταν τη βλέπω = when I see her

So the whole sentence has:

1. a main clause: Χαμογελάω στη φίλη μου
2. a time clause: όταν τη βλέπω στο πανεπιστήμιο

This is a very common structure in Greek.

In Greek, the present tense often expresses habitual or repeated actions, just like in English.

So:

• Χαμογελάω ... όταν τη βλέπω ... means
  I smile ... when I see her ...

This suggests something that happens regularly or generally, for example every time the speaker sees her at the university.

Greek present tense can cover:

• what is happening now
• what happens regularly
• general habits

στο πανεπιστήμιο means at the university or sometimes to the university, depending on context.

Here it means at the university, because it tells you where the speaker sees her:

• όταν τη βλέπω στο πανεπιστήμιο = when I see her at the university

Again, στο is a contraction:

• σε + το → στο

Usually πανεπιστήμιο specifically means university.

If a learner is translating from English, it is good to know that English college does not always match Greek πανεπιστήμιο exactly. In this sentence, though, the normal meaning is university.

You may also see χαμογελώ.

Both mean I smile. In modern Greek, both forms exist, and speakers may prefer one or the other depending on style, habit, or region.

So these are both possible dictionary forms:

• χαμογελάω
• χαμογελώ

In your sentence, Χαμογελάω is completely normal.

A helpful breakdown is:

• Χαμογελάω = I smile
• στη φίλη μου = at my friend
• όταν = when
• τη βλέπω = I see her
• στο πανεπιστήμιο = at the university

So the structure is:

I smile at my friend when I see her at the university.

Main verb first, then the person smiled at, then the time clause.

Yes. Greek word order is more flexible than English, although the original sentence is very natural.

For example, you could also hear:

• Όταν τη βλέπω στο πανεπιστήμιο, χαμογελάω στη φίλη μου.

This puts more emphasis on the when clause first:

• When I see her at the university, I smile at my friend.

The original version is still the most straightforward for learners.

A rough pronunciation guide is:

• Cha-mo-GHE-la-o sti FEE-li moo O-tan ti VLE-po sto pa-ne-pi-STI-mio

A few useful points:

• χ is like the h sound in huge for many learners, but rougher
• γ before ε/ι is a softer sound than English g
• β is pronounced like English v
• ω and ο are both pronounced o in modern Greek

The stress marks are important:

• χαμογελάω
• φίλη
• βλέπω
• πανεπιστήμιο

Because it says τη φίλη μου with the article-like form built into the phrase, it usually sounds like my friend in a definite, specific sense.

Greek often uses the article with possessives:

• η φίλη μου = my friend
• το βιβλίο μου = my book

So the sentence most naturally suggests a particular friend the speaker has in mind.