Learn Hardcore Finnish: Suosittu kahvila on yleensä täynnä.

It’s in the nominative singular, the basic form used for the subject of a sentence. Since kahvila is the thing “being full,” it remains in nominative.

What is suosittu and how does it agree with kahvila?

Suosittu is a past participle used as an adjective meaning popular. Adjectives in Finnish agree in case, number and sometimes in mood with the noun they modify. Here both suosittu and kahvila are nominative singular.

What role does on play in this sentence?

On is the third-person singular present form of olla (to be). It acts as the copula linking subject (suosittu kahvila) and predicate (täynnä), so it simply means is.

What kind of word is yleensä, and why is it placed between on and täynnä?

Yleensä is an adverb of frequency meaning usually. In Finnish the typical position for adverbs is right after the finite verb. For emphasis you could front it (Yleensä suosittu kahvila on täynnä), but the default spot is between on and täynnä.

What kind of word is täynnä, and why isn't täysi used here?

Täynnä is the predicative form of the adjective täysi (full), often called an essive or adverbial adjective. After a copula like on, you use täynnä to mean is full. If you add what it’s full of, that thing goes in the partitive:

Suosittu kahvila on täynnä ihmisiä (is full of people).

How would you make the sentence plural?

Change suosittu → suositut, kahvila → kahvilat, and on → ovat:
Suositut kahvilat ovat yleensä täynnä.

How do you pronounce Suosittu kahvila on yleensä täynnä?

IPA: /ˈsuo̯sitːu ˈkɑhʋilɑ on ˈyleensä ˈtæynnæ/
Rough guide:

“suo” like English “swo”
double tt is held longer than single t
kahvila has a clear h and v
y as in French “u” (rounded front vowel)
ä like the “a” in “cat”