Learn Finnish: Neiti sihteeri kirjoittaa viestin. - Miss Secretary writes the message.

Viestin is the total object (accusative case ending in -n). This shows that the action is seen as complete: she writes the entire message. If you used the partitive viestiä, it would emphasize an ongoing process, meaning she is currently writing a message.

Both neiti and sihteeri are in the basic nominative form. Do titles always match the noun they modify?

Yes, usually. When a title like neiti (Miss) is paired with a name or profession, they typically act as a single unit and take the same case. Since the person is the subject of this sentence, both words stay in the nominative case.

Does the verb kirjoittaa look exactly the same here as it does in the dictionary?

Yes, it does! The infinitive (dictionary form) is kirjoittaa. To get the third-person singular (he/she) form for Type 1 verbs, you take the strong stem (kirjoitta-) and double the final vowel. This makes it kirjoittaa, which happens to be identical to the infinitive.