Learn Spanish (Latin America): Su táctica nos hizo ganar el partido.

In Spanish, to say you "make someone do something," you use a causative structure: the verb hacer followed directly by an infinitive verb (here, ganar). You don't conjugate the second verb. The people who are made to do the action are represented by an object pronoun (here, nos), which comes right before the conjugated form of hacer.

Could the "nos" be attached to the end of the infinitive, like "hizo ganarnos"?

No. In this specific structure, the pronoun representing the people being caused to act (nos) belongs to hacer and goes before it. If you wrote hizo ganarnos, it would actually mean "he made [someone] win us," turning "us" into the prize being won!

I learned that trying to influence someone's actions requires the subjunctive. Why use the infinitive ganar here?

You are right that verbs of influence often trigger the subjunctive, specifically when you use que (like hizo que ganáramos - "he made it so that we won"). However, when you drop the que and use hacer with an object pronoun, you just use the infinitive. Both structures are correct, but the infinitive is very common for direct causes like this.

How do we know su táctica means "his tactic"? Could it mean "her tactic" or "their tactic"?