How do I know that this is "his" room and not "her" or "their" room?

Bonjour Yvonne !

When you say "Il y a un lit dans sa chambre.", the possessive sa could indeed refer to either "his" or "her" room, as the gender of the possessive adjective is determined by the possession , and not the owner.

Without a clear context, in French there is no way for you to know the gender of the owner from the possessive adjective !

Have a look at our related lessons:
https://progress.lawlessfrench.com/revision/grammar/common-mistakes-with-mon-ma-mes-ton-ta-tes-and-son-sa-ses-possessive-adjectives
https://progress.lawlessfrench.com/revision/grammar/use-notre-nos-votre-vos-leur-leurs-to-say-our-your-and-their-possessive-adjectives

I hope that's helpful!
À bientôt !