Learn German: Der Bär wurde jenseits des Tals gesehen. - The bear was seen beyond the valley.

The preposition jenseits (beyond / on the other side of) requires the genitive case. Because Tal is a neuter noun (das Tal), the definite article becomes des and we add an -s to the end of the noun.

Would it also be correct to write des Tales?

Yes, absolutely. For one-syllable neuter and masculine nouns, the genitive ending can be either -s or -es. des Tals is more common in modern, everyday German, while des Tales sounds slightly more traditional or formal.

How exactly is the passive voice constructed here with wurde?

The sentence uses the simple past (Präteritum) passive. You form this by taking the simple past of the helping verb werden (which is wurde for a singular third-person subject like der Bär) and placing the past participle of the main verb (gesehen) at the very end of the sentence.

What is the exact opposite of jenseits if the bear were on our side of the valley?

You would use the preposition diesseits, which means 'on this side of.' The sentence would then be Der Bär wurde diesseits des Tals gesehen. Like jenseits, it also requires the genitive case.