We use would + infinitive without to in the main clause of the second/unreal conditional to talk about possible results of an uncertain situation:
I wouldn’t have to work hard if I was rich.
What would you do if you lost your passport?
We use would have + past participle in the main clause of the third/unreal conditional to talk about the theoretical results of a situation that did not happen:
I would have taken a picture of the Loch Ness monster if I had seen it.
If I had lived a hundred years ago, I wouldn’t have traveled by air.
In informal writing and spoken English we often use the short form ‘d.
Look at the lyrics of your favorite songs and try to find phrases with would in the second and the third conditionals in them.
I’d rather be a sparrow than a snail… (El Condor Pasa).
No one would have believed in the last years of the nineteenth century that… (War of the Worlds).