Learn Russian: Добрый день! Я студентка.

In Russian, the present tense of the verb "to be" (am, is, are) is usually left out. You simply put the pronoun and the noun together, literally saying "I student."

How do we know the speaker is female?

The word студентка specifically means a female student. It is formed by adding the feminine ending -ка to the masculine word студент. A male speaker would just say Я студент.

Does Добрый день literally translate to "Good afternoon"?

It literally means "Good day" (Добрый means good or kind, and день means day). Russians use this as the standard greeting during the daytime, which is why it is often translated as "Good afternoon" in English.

Why does the adjective Добрый end with -ый?

Russian adjectives change their endings to match the gender of the noun they describe. Because день is a masculine noun, the adjective Добрый takes the standard masculine ending -ый.