Learn Hardcore Finnish: Innostunut opiskelija on kahvilassa.

Finnish does not have articles like a/an or the at all.
Whether you translate innostunut opiskelija as an excited student or the excited student depends entirely on context, not on any word in the Finnish sentence.

So:

Innostunut opiskelija on kahvilassa.
can mean:
- An excited student is in the café.
- The excited student is in the café.

Context (what has already been mentioned, what both speakers know) tells you which English article to choose.

What exactly is on here? Is it a separate verb like is?

Yes. On is the 3rd person singular present form of the verb olla (to be).

The basic present-tense forms are:

minä olen – I am
sinä olet – you are (singular)
hän on – he/she is
me olemme – we are
te olette – you are (plural / polite)
he ovat – they are

So in your sentence, on means is (or there is, depending on word order, see below).

Why is there no word for he/she in the sentence?

Finnish often drops subject pronouns when the subject is clear from the verb form or the context.

Here, the subject is innostunut opiskelija, so there is no need for hän (he/she).
You normally do not say:

✗ Hän innostunut opiskelija on kahvilassa.

The sentence already has its subject: innostunut opiskelija. Adding hän would be ungrammatical here.

Why is the adjective innostunut in front of opiskelija? Is that the normal order?

Yes. In Finnish, descriptive adjectives usually come before the noun they modify, just like in English:

innostunut opiskelija – excited student
väsynyt opettaja – tired teacher
suuri talo – big house

So innostunut opiskelija is an attributive use of the adjective: it directly modifies the noun.

Important points:

The adjective matches the noun in number and case:
- innostunut opiskelija – singular nominative
- innostunut opiskelija on kahvilassa.
- innostuneet opiskelijat – plural nominative
- innostuneet opiskelijat ovat kahvilassa.

Later you’ll also see matching case endings, e.g. innostuneen opiskelijan (genitive singular), but here both are in basic (nominative) form.

What does the form innostunut really mean? It looks like a past participle.

You are right: innostunut is historically a past participle of the verb innostua (to get excited). But in modern Finnish, forms like this are very often used as regular adjectives.

So:

As a verb-like meaning:
Opiskelija on innostunut. – The student has become excited / is excited.
As an adjective before a noun:
innostunut opiskelija – an excited student.

In your sentence, innostunut is functioning purely as an adjective that describes opiskelija.

What does kahvilassa literally mean, and what is the -ssa ending?

The base word is kahvila – café.
The ending -ssa / -ssä is the inessive case, which usually means in or inside.

So:

kahvila – café
kahvilassa – in the café, at the café (physically inside / in that place)

Rough breakdown:

kahvila (stem: kahvila-)
kahvila
- ssa → kahvilassa – in a/the café

What is the difference between kahvila, kahvilassa, kahvilaan, and kahvilasta?

These are different cases expressing location and movement:

kahvila – café (basic form, like dictionary form)
kahvilassa – in the café (inessive: where something is)
kahvilaan – into the café / to the café (illative: movement into)
kahvilasta – from the café (elative: movement out of / from)

Examples:

Opiskelija on kahvilassa. – The student is in the café.
Opiskelija menee kahvilaan. – The student goes to/into the café.
Opiskelija tulee kahvilasta. – The student comes from the café.

Can I also say Kahvilassa on innostunut opiskelija? Does that change the meaning?

Yes, that is a perfectly correct sentence, and the nuance changes slightly.

Innostunut opiskelija on kahvilassa.
- Focus is more on the excited student.
- Often understood as The excited student is in the café (as opposed to somewhere else).
Kahvilassa on innostunut opiskelija.
- Focus is more on the café and what is there.
- Often understood as There is an excited student in the café.

So Finnish word order is flexible, but it affects emphasis and information structure. Both sentences are grammatical and natural, but they highlight different parts of the information.

Why are innostunut and opiskelija in their basic forms (no ending) even though one describes the other?

Because they are in the nominative singular, which is the basic dictionary form, used here for:

the subject: innostunut opiskelija
an attributive adjective that modifies that subject: innostunut

In Finnish:

A noun that functions as a straightforward subject is typically nominative.
An adjective that directly modifies that noun shares its number and case.

Example parallels:

Nuori mies on kotona. – The young man is at home.
- nuori (young) – nominative singular
- mies (man) – nominative singular

Same pattern: innostunut opiskelija.

How would I say The student is excited (not “the excited student”)?

You change innostunut from an adjective before the noun to a predicative adjective after the verb:

Opiskelija on innostunut. – The student is excited.

Compare:

Innostunut opiskelija on kahvilassa. – The excited student is in the café.
(Adjective before noun, acts like part of the noun phrase.)
Opiskelija on innostunut kahvilassa. – The student is excited in the café.
(Now innostunut describes the state the student is in.)

How do I negate this sentence: The excited student is not in the café?

Use the negative verb ei plus the base form ole (from olla):

Innostunut opiskelija ei ole kahvilassa.
– The excited student is not in the café.

Pattern:

positive: opiskelija on – the student is
negative: opiskelija ei ole – the student is not

How should I pronounce innostunut and kahvilassa? Anything tricky?

Key points:

Stress is always on the first syllable in Finnish.
- IN-no-stu-nut
- KAH-vi-las-sa
Double consonants are held longer:
- In kahvilassa, the ss is a long s, so hold it slightly longer than a single s.
- Length can change meaning in Finnish, so s vs ss matters.
Vowels are pure and clear (no diphthonging like in English).
Say each vowel cleanly: i, a, u, o are all distinct and not reduced.