Learn Hardcore Turkish: Arşiv burada.

Turkish normally omits the present-tense copula 'to be'. In sentences like Arşiv burada the meaning 'is' is implied. If you want to include it—for emphasis or formality—you could say Arşiv buradadır (literally 'Archive here-is').

How is burada formed? What does the -da suffix mean?

burada breaks down as:

bura: an informal root meaning 'this place'
-da: the locative suffix meaning 'at/in'

Because u is a back vowel, it takes -da (not -de). So bura + ‑da = burada, 'at here' = here.

Why is the word order Arşiv burada (Subject + Adverb) instead of the typical SOV?

Turkish default word order is SOV, but when the copula is dropped you get a nominal sentence: Subject + adverbial modifier (location).
So Arşiv (subject) + burada (where) = 'The archive is here.'

Why isn't there an article like the or a/an before Arşiv?

Turkish has no definite or indefinite articles. Nouns stand alone:

To express indefiniteness you can use bir, e.g. Burada bir arşiv var = 'There is an archive here.'
To point to a specific archive, just Arşiv burada = 'The archive is here.'

What's the difference between burada and burası?

burada is an adverb meaning 'here (at this place)'.
burası is a demonstrative pronoun meaning 'this place'.

You say Arşiv burada ('The archive is here').
You could say Burası arşivdir ('This place is an archive') if you want to use burası.

What about Arşiv buradadır—how is that different?

Adding the copula suffix -dır to burada gives buradadır, literally 'is here':

Arşiv buradadır = 'The archive is here' (slightly more formal or emphatic).
Dropping -dır (i.e. Arşiv burada) is more neutral or conversational.

How do you pronounce Arşiv, and where is the stress?

ş is pronounced like English sh in 'shoe'.
Arşiv is [ar-ʃiv].
Turkish words are generally stressed on the final syllable, so the primary stress falls on -şiv.

What's the difference between Arşiv burada and Burada bir arşiv var?

Arşiv burada = 'The archive is here' (referring to a known, specific archive).
Burada bir arşiv var = 'There is an archive here' (introducing the existence of an archive, indefinite).