Προχωράω προς την πλατεία και μετά στρίβω αριστερά.

Greek often drops subject pronouns when they are not needed. The verb ending already tells you who the subject is.

• Προχωράω = I go forward / I continue / I walk on
• στρίβω = I turn

So Greek does not need εγώ (I) here. You could say Εγώ προχωράω..., but that usually adds emphasis, like I go forward.

προς means towards or in the direction of. It is commonly followed by the accusative case.

So:

• προς = towards
• την πλατεία = the square (accusative)

Together, προς την πλατεία means towards the square.

A learner might compare it with English to or towards, but in Greek προς specifically gives a sense of movement in the direction of something.

Because Greek usually uses the definite article much more often than English. Here την means the.

• η πλατεία = the square (nominative)
• την πλατεία = the square (accusative)

Since προς takes the accusative, η πλατεία changes to την πλατεία.

Good question: the article changes clearly, but the noun itself does not always change form in a visible way.

For this noun:

• η πλατεία = nominative
• την πλατεία = accusative

The noun πλατεία looks the same in both cases in the singular, but the article shows the case change:

• η → nominative
• την → accusative

This is very common in Modern Greek.

It can mean several related things depending on context:

• go forward
• move on
• walk on
• continue straight ahead

In directions, Προχωράω often means something like I keep going or I go on.

It is not always identical to πηγαίνω (I go).
προχωράω suggests forward movement / continuing ahead, which fits directions very naturally.

Yes, in everyday Modern Greek these are usually just two forms of the same verb.

You may see:

• προχωράω
• προχωρώ

Both mean I move forward / I proceed.

Similarly:

• αγαπάω / αγαπώ
• ρωτάω / ρωτώ

In normal speech, προχωράω is very common and natural.

Here μετά means then, after that, or next.

So:

• και = and
• μετά = then / after that

Together, και μετά means and then.

In directions, this is a very common way to link steps:

• Προχωράω προς την πλατεία και μετά στρίβω αριστερά.
• I continue towards the square and then turn left.

Because αριστερά here is being used as an adverb, meaning left in the sense of to the left / leftwards.

So:

• στρίβω αριστερά = I turn left
• στρίβω δεξιά = I turn right

This is the normal Greek pattern.

Compare:

• αριστερά = left / on the left / leftwards
• η αριστερά = the left (as a noun, in some contexts)

In directions, you usually just say στρίβω αριστερά.

They are in the present tense, first person singular.

• Προχωράω = I go forward / I continue
• στρίβω = I turn

In Greek, the present tense is often used for:

• what someone is doing now
• habitual actions
• giving directions step by step in a vivid, immediate way

So even though English might sometimes prefer Go towards the square and then turn left, Greek can naturally say it with the present tense.

Yes, but then Greek would normally use the imperative, not the first person singular.

For example:

• Προχώρα προς την πλατεία και μετά στρίψε αριστερά.

That means Go towards the square and then turn left.

Your original sentence is in the first person: I continue... and then I turn...
The imperative version is used for giving directions to someone else.

Not completely. Greek word order is fairly flexible, although some orders sound more natural than others.

This sentence:

• Προχωράω προς την πλατεία και μετά στρίβω αριστερά.

is very natural.

You might also hear:

• Προχωράω προς την πλατεία, μετά στρίβω αριστερά.
• Μετά στρίβω αριστερά.

But the original version is a very standard, smooth way to say it.

Usually, yes. στρίβω commonly means turn in movement and direction contexts.

Examples:

• στρίβω αριστερά = turn left
• στρίβω δεξιά = turn right

But in other contexts it can also mean things like twist or bend, depending on what is being talked about. In your sentence, it clearly means turn while moving.

A rough pronunciation guide is:

• Προχωράω ≈ pro-ho-RA-o
• προς ≈ pros
• την ≈ tin
• πλατεία ≈ pla-ti-A
• και ≈ ke
• μετά ≈ me-TA
• στρίβω ≈ STREE-vo
• αριστερά ≈ a-ri-ste-RA

A few helpful points:

• The stress marks show which syllable is stressed.
• αι is usually pronounced like e.
• στρ at the beginning of στρίβω can feel difficult at first for English speakers, but it is a normal Greek cluster.

Yes, it sounds natural and neutral. It is the kind of Greek you could hear or use when:

• describing a route
• explaining where you go
• narrating your movements

It is neither especially formal nor especially slangy.