Learn Russian: Она ждёт письмо от этого нового друга. - She is waiting for a letter from this new friend.

In Russian, the word you use for "from" depends on the source. You use от when receiving something from a person (like от друга). You use из when something comes from inside a place or container (like из школы - from school).

Why do the words for "this" and "new" end in -ого?

The preposition от always requires the genitive case. Because the noun друг (friend) is masculine, the demonstrative pronoun этот (this) and the adjective новый (new) must match it. They both drop their nominative endings and take the masculine genitive ending -ого, becoming этого нового.

How do I pronounce the -ого endings in этого and нового?

In Russian, the letter г in the genitive endings -ого and -его is always pronounced like an English "v" (в). So, you should pronounce этого like "eh-tuh-vuh" and нового like "noh-vuh-vuh".

What case is письмо in here? Doesn't the verb ждать sometimes take the genitive case?