Learn Russian: Я говорю по-русски.

The dictionary form (infinitive) is говорить (to speak). Because it ends in -ить, it follows the second conjugation pattern you are currently learning. To make the 'I' (я) form, you drop the -ить and add the ending -ю, which gives us говорю.

Why do we use по-русски instead of the regular word for 'Russian' (русский)?

When describing how you speak, read, or write a language, Russian uses a special adverb form. It combines the prefix по- with an -и at the end. Literally, you are saying 'I speak in a Russian way'. You would only use the regular adjective русский to describe nouns, like русский чай (Russian tea).

Does the dash in по-русски always have to be there?

Yes! Adverbs made for languages using the по- prefix and -и ending are always hyphenated. You will also see this exact same pattern with other languages, like по-английски (in English) or по-испански (in Spanish).

Why isn't по-русски capitalized like languages are in English?

In Russian, the names of languages, nationalities, and days of the week are always written in lowercase letters unless they happen to appear at the very beginning of a sentence.