Learn Hardcore Greek: Μετά τρώμε γλυκό στο σπίτι.

In this sentence Μετά is an adverb meaning then / afterwards in a sequence of actions.
It does not mean after [something] here; it just links events in time: First we do X, μετά τρώμε γλυκό… = then we eat dessert….
When μετά means after [something], it is usually followed by a noun or phrase, e.g. μετά το μάθημα = after the lesson, μετά από δύο ώρες = after two hours.

Why is there no word for we in the sentence?

Greek normally leaves out subject pronouns like εμείς (we) because the verb ending already shows the person and number.
The form τρώμε can only mean we eat, so εμείς is not needed.
You would add εμείς only for emphasis or contrast, e.g. Εμείς μετά τρώμε γλυκό στο σπίτι, όχι έξω. = We (on the other hand) then eat dessert at home, not out.

Why is the verb τρώμε in the present tense if in English we might say “then we will eat dessert”?

Greek often uses the present tense for planned or sequential future actions, especially when describing a routine, program, or instructions.
So Μετά τρώμε γλυκό στο σπίτι can be understood as Then we eat / we’ll eat dessert at home depending on context.
If you want to make the future very explicit, you can say Μετά θα φάμε γλυκό στο σπίτι (Then we will eat dessert at home), using θα with the future stem φάμε.

Why is there no article before γλυκό? Why not το γλυκό?

Without an article, γλυκό has a more general or indefinite meaning, similar to dessert / some dessert.
So τρώμε γλυκό ≈ we eat (some) dessert or we have dessert.
If you say τρώμε το γλυκό, you usually mean we eat the dessert referring to a specific, known dessert (for example, the one someone has just prepared or mentioned).

Does γλυκό here mean “sweet” as an adjective, or “dessert” as a noun?

Here γλυκό is a noun, meaning a sweet / a dessert.
It comes from the adjective γλυκός (sweet), but Greek often turns adjectives into neuter nouns to name things:

γλυκό = a sweet thing, a dessert
το κρύο = the cold
το ζεστό (in context) = the hot drink, etc.
So τρώμε γλυκό means we eat dessert, not we eat something sweet in general.

Could I say γλυκά instead of γλυκό? What would change?

Yes. γλυκά is the plural: sweets / candies / desserts (more than one).

τρώμε γλυκό = we eat (some) dessert / a dessert (singular, general)
τρώμε γλυκά = we eat sweets / lots of sweet things (plural)
Both are correct; you choose based on whether you’re thinking of one dessert or various sweet items.

What does στο mean, and how is it formed?

Στο is a contraction of the preposition σε (in, at, to) and the neuter definite article το (the).
So σε + το = στο, literally in/at/to the.
In στο σπίτι, it literally means in/at the house, which in natural English is at home.

What’s the difference between στο σπίτι and just σπίτι?

Both can mean at home, but there is a slight nuance:

στο σπίτι (literally at the house) is a bit more explicit/neutral and is very common.
σπίτι without an article often feels a bit more colloquial or short, like English I’m home vs I’m at home.
So Μετά τρώμε γλυκό στο σπίτι and Μετά τρώμε γλυκό σπίτι can mean the same, but the first is more standard.

How would I say “at our house” or “at my house” in this sentence?

You add the possessive pronoun after σπίτι:

Μετά τρώμε γλυκό στο σπίτι μας. = Then we eat dessert at our house.
Μετά τρώμε γλυκό στο σπίτι μου. = Then we eat dessert at my house.
In many contexts Greek leaves μας / μου out because it’s obvious whose house it is, just like English often understands home as our home.

Is the word order fixed, or can I move Μετά and στο σπίτι around?

Word order in Greek is fairly flexible, especially for adverbs and prepositional phrases.
For example, all of these are grammatically correct:

Μετά τρώμε γλυκό στο σπίτι.
Τρώμε μετά γλυκό στο σπίτι.
Τρώμε γλυκό στο σπίτι μετά.
Μετά στο σπίτι τρώμε γλυκό.
The basic meaning stays the same; changing the order can slightly shift emphasis (for example, putting στο σπίτι earlier can highlight the location).

Which case is γλυκό in here, and how can I tell?

Γλυκό is in the accusative case, functioning as the direct object of the verb τρώμε.
For neuter nouns like γλυκό, the nominative and accusative forms are identical, so you know the case from the role in the sentence and usual word order: subject–verb–object.
Here (εμείς) τρώμε γλυκό clearly has γλυκό as what is being eaten, so it’s accusative.

Could I use another word instead of Μετά, like Ύστερα or Αργότερα?

Yes. Common alternatives are:

Ύστερα τρώμε γλυκό στο σπίτι. – very similar to Μετά, also then / afterwards.
Αργότερα τρώμε γλυκό στο σπίτι. – later, often suggesting a bit more time passes.
All are correct; μετά and ύστερα are often interchangeable in casual speech, while αργότερα usually implies later on, not immediately next.

Is there a more formal word for “dessert” than γλυκό?

Yes, the more formal or “restaurant menu” word is επιδόρπιο.
So you could say Μετά τρώμε επιδόρπιο στο σπίτι, which literally means Then we eat dessert at home, in a more formal register.
In everyday speech, though, γλυκό is by far the more common word for dessert.