Learn Farsi: آنها باختند و ما پیروز شدیم.

In the simple past tense, we add personal endings to the past stem of a verb. The past stem here is باخت (lost). To say "they" did it, we add the suffix ـند (-and), making it باختند.

Why is "we won" translated using two words (پیروز شدیم)?

Farsi uses many compound verbs. "To win" is literally "to become victorious", made of the word پیروز (victorious) and the helper verb شدن (to become). In the simple past for "we", you only change the helper verb, which becomes شدیم (we became). It combines the past stem شد and the "we" ending ـیم.

Could I just say باختند و پیروز شدیم without the pronouns آنها and ما?

Yes, absolutely! Since the verb endings (ـند for "they" and ـیم for "we") already tell you exactly who is doing the action, the pronouns are optional. Using them here just adds a bit of contrast or emphasis, like saying "THEY lost and WE won."

I've learned that و means "and", but how is it pronounced here in everyday speech?

Although it is formally pronounced "va", in spoken Farsi it usually sounds like a quick "o" connecting the words. So instead of "bakhtand va ma", you will typically hear "bakhtand-o ma".