Would have is correct.
Would of is not correct.
However, “would of” has crept into the language because when “would have” is abbreviated to “would’ve”, and spoken out loud, it sounds like “would of”.
“She would have gone out, but she didn’t have anything to wear.”
“She would’ve gone out, but she didn’t have anything to wear.”
This works throughout the range of words – “might have”, “would have”, “should have”, etc.
For more troublesome pairs, choose the category from the cloud over to your right, or click here.