Learn Hardcore Polish: Herbata z wanilią smakuje dobrze.

Because the preposition z/ze (“with”) always requires the instrumental case in Polish. So wanilia (nominative) becomes wanilią (instrumental) to express “with vanilla.”

Why do we use the adverb dobrze instead of the adjective dobry?

In Polish you use an adverb to describe how something tastes. Dobrze is the adverbial form of dobry. Adjectives like dobry modify nouns, adverbs modify verbs.

Why is there no article before herbata? In English we say the tea or a tea.

Polish does not have definite or indefinite articles (no equivalents of the, a/an). You simply use the noun by itself and rely on context.

Could I say Herbata z wanilią smakuje pysznie instead of smakuje dobrze?

Yes. pysznie (“deliciously”) is another appropriate adverb. You can swap dobrze for other adverbs like świetnie, doskonale, wspaniale to express different degrees of tastiness.

What’s the difference between Herbata jest dobra and Herbata smakuje dobrze?

Herbata jest dobra: “The tea is good.” Here dobra is an adjective describing the tea’s general quality.
Herbata smakuje dobrze: “The tea tastes good.” Here dobrze is an adverb describing the action of tasting.

Can I change the word order? For example, Herbata z wanilią dobrze smakuje?

Yes. Polish has flexible word order. All of these are correct and just shift emphasis slightly:

Herbata z wanilią dobrze smakuje.
Z wanilią herbata smakuje dobrze.
Herbata smakuje dobrze z wanilią.

Is smakuje the present tense of smakować? Could we say smakuje się?

Smakuje is the 3rd person singular present of smakować (“to taste”). You do not add się here, because smakuje się would form an impersonal construction meaning “one tastes” rather than “the tea tastes.”