Learn Turkish: Beyaz formayı giymedik, oysa giyseydik kazanırdık. - We didn't wear the white jersey; whereas if we had worn it, we would have won.

This is the past counterfactual conditional (Type 3). It is built from the verb root giy- (wear), plus the conditional suffix -se (if), the buffer letter -y-, the past tense -di, and the 'we' ending -k. Together, giyseydik means 'if we had worn [it]', describing a condition in the past that didn't actually happen.

How does kazanırdık translate to 'we would have won'?

The main result clause of a past unreal 'if' sentence usually uses the aorist (broad tense) combined with the past tense. Here, it breaks down into kazan- (win) + -ır (aorist) + -dı (past) + -k (we). While in other contexts this combination means 'we used to win', in an 'if' sentence it translates to 'we would have won'.

What exactly does oysa mean here, and could I just use ama (but) instead?

Oysa translates to 'whereas', 'however', or 'but in fact'. You absolutely could use ama here, and the sentence would still make perfect sense. However, oysa adds a bit more dramatic contrast, heavily emphasizing the difference between the actual reality (we didn't wear it) and the missed opportunity.

The English translation says 'if we had worn it', but there is no word for 'it' before giyseydik. Why?