Learn Icelandic: Ég tala íslensku.

Íslenska is the basic dictionary form. However, in this sentence it is the direct object receiving the action of the verb tala (to speak). This means it changes into the accusative case, and the -a at the end becomes a -u.

Does the verb tala change if the subject changes?

Yes! Icelandic verbs change their endings depending on who is doing the action. While 'I speak' is ég tala, 'you speak' would be þú talar, and 'he or she speaks' is hann eða hún talar.

Why isn't íslensku written with a capital letter?

In Icelandic, the names of languages, nationalities, and days of the week are not capitalized unless they appear at the very beginning of a sentence. So, while we write 'Icelandic' in English, it is just íslenska (or íslensku) in Icelandic.