Black Ninja here. Don’t ever write “would of.” Just don’t. I can’t imagine a situation where “would of” would ever be correct, and I have an amazing Ninja imagination. Actually, my keen Ninja intellect just thought of one sentence where you can say it:
“Don’t ever write ‘would of.'”
There, that’s it.
So why do so many people use this expression? You might say that it’s because “would of” and “would’ve” sound similar, but I think it’s because they’re not Ninjas.
So what is correct? As alluded (ooh big word) to above, “would’ve” is how it’s spelled. A contraction for “would have.” As in “I would’ve known how to write ‘would’ve’ if I were a Ninja.” Well, you don’t actually have to be a Ninja, you just have to listen to them.