Learn Turkish: İyi ki yanılmadın, yoksa kaza yapacaktık. - Fortunately you were not mistaken, otherwise we would have had an accident.

No, and that is what makes it easy to use! İyi ki (fortunately / it is a good thing that) simply goes in front of a regular, conjugated verb. Here it pairs with the standard past tense yanılmadın (you were not mistaken) to express relief about a fact.

Why use yapmak (to make/do) with kaza?

In Turkish, you do not "have" a car accident like you do in English; you "make" one. The fixed expression for getting into an accident is kaza yapmak.

How does yapacaktık translate to "we would have had"?

Yapacaktık combines the future suffix -acak and the past tense suffix -tı (followed by the "we" ending -k). Literally meaning "we were going to do," this future-in-the-past combination is exactly how Turkish expresses "would have" for something that was set to happen but was ultimately avoided.

Doesn't yoksa literally mean "if there isn't"? How does it mean "otherwise"?

Exactly! It is made of yok (non-existent / there is not) and the conditional suffix -sa (if). While literally meaning "if it is not so," it has become the standard conjunction for "otherwise" or "or else" to introduce what would happen if the first statement weren't true.