Learn Swedish: Om du hade varnat mig, skulle jag inte ha gjort det. - If you had warned me, I would not have done it.

This is the V2 (verb-second) rule in action. The entire Om (if) clause counts as the first piece of information in the sentence. To keep the verb in the second position, the main clause must start immediately with the verb skulle, followed by the subject jag.

How exactly do you form the 'would have done' part of the sentence?

Swedish builds this unreal past conditional just like English does. You use skulle (would) plus ha (have) plus the supinum form of the main verb, which in this case is gjort (done).

Why is inte placed where it is?

In a main clause, sentence adverbs like inte come after the first verb and the subject. Since this clause has inverted word order, the first verb is skulle and the subject is jag, making inte land right after them. If this were a subordinate clause, inte would come before the verb instead.

Why does varna become varnat here?

Because it follows hade (had). Together they form the past perfect tense. Varna is a regular Group 1 verb, and all Group 1 verbs end in -at in their supinum form.