Learn Russian: Они живут там три года. - They have been living there for three years.

This is the focus of your current lesson! After the numbers два (2), три (3), and четыре (4), Russian nouns must take the genitive singular form. Since год (year) is a masculine noun ending in a consonant, we add an -а to the end to make it года.

The English translation says "have been living," but isn't живут just the present tense?

Exactly. English uses "have been living" to show an action that started in the past and is still happening today. Russian is much simpler here: if the action is still happening right now, you just use the present tense. So Они живут covers both "They live" and "They have been living".

Why isn't there a Russian word for "for" in "for three years"?

To express how long an action lasts, Russian usually doesn't need a preposition like "for". You just state the amount of time directly next to the verb. So, the phrase три года by itself perfectly translates to the duration "for three years".

I remember the dictionary form is жить (to live). Where does the -в- in живут come from?