Learn Finnish: Vuosisata sitten ihmiset etsivät työtä monista maista. - A century ago, people searched for work in many countries.

The postposition sitten (ago) takes the nominative case when you are talking about exactly one of something, like a single century (vuosisata). If you were talking about multiple centuries, you would use the partitive case, for example: kaksi vuosisataa sitten (two centuries ago).

Why is the word for work (työ) in the partitive case (työtä)?

The verb etsiä (to search for) is a partitive verb. Because searching is an ongoing action and you might not actually find what you are looking for, the object of the search must always be in the partitive case.

The translation says "in many countries", but monista maista uses the elative ending (-sta) which means "out of". Why?

In Finnish, verbs related to searching (etsiä) or finding (löytää) require "from" cases. Instead of saying you search "in" a place, the Finnish logic is that you are trying to search or dig something out of that place.

Does etsivät mean "they search" (present) or "they searched" (past)?

In this sentence, it means "they searched". For the verb etsiä, the present tense and the past tense (imperfect) look exactly the same in the "they" form: he etsivät. You have to rely on the context—like the phrase vuosisata sitten (a century ago)—to know it's in the past.