Learn French: Assoiffés, ce sont eux qui ont cherché l'oasis. - Thirsty, they are the ones who looked for the oasis.

Assoiffés is an apposition (a detached adjective). It modifies and agrees with the emphatic pronoun eux later in the sentence. Placing it at the very beginning elegantly creates an implied cause, meaning 'Because they were thirsty...'

Why do we say ce sont eux rather than c'est eux?

When using the emphatic structure to mean 'they are the ones who', the verb être must match a third-person plural pronoun or noun. Since eux is third-person plural, c'est becomes ce sont. Note that in casual spoken French you will often hear c'est eux, but ce sont eux is the grammatically correct written standard.

The subject of ont cherché is the word qui, so how do we know which conjugation to use?

The relative pronoun qui acts as the subject, but it always takes its conjugation from the noun or pronoun it replaces (its antecedent). Since qui refers back to eux (they), the auxiliary verb avoir is conjugated in the third-person plural as ont.

Why is there no French word for 'for' in ont cherché l'oasis?