Learn Hardcore Icelandic: Þetta er íslenska.

Þetta: [ˈθɛht̪a] — roughly THEHT-ta (voiceless th as in thing; Icelandic tt is preaspirated, so you hear a little breath before the t)
er: [ɛr] — ehr (short e, trilled or tapped r)
íslenska: [ˈislɛnska] — EES-lens-ka (stress on the first syllable; long í like English ee)

What does each word mean?

Þetta = this (neuter demonstrative pronoun)
er = is (3rd person singular of að vera, to be)
íslenska = Icelandic (the language; a feminine noun)

Why is íslenska not capitalized?

Languages in Icelandic are not capitalized unless they begin a sentence. So íslenska is lowercase by default. This differs from English, which capitalizes language names.

Why is there no word for “a” or “the” here?

Icelandic has no separate indefinite article (no equivalent of “a/an”). The definite article is a suffix. Compare:

íslenska = Icelandic (language), general/indefinite
íslenskan = the Icelandic (language), definite

Which case is in, and why?