The conditional perfect, would have, refers to a missed opportunity in the past. In informal speech, it contracts to would’ve, not "would of."
I would have (would’ve) liked to see that movie.
I would of liked to see that movie.
She would have (would’ve) told me if that happened.
She would of told me if that happened.
If you had asked me, I would have (would’ve) tried to help.
If you had asked me, I would of tried to help.
Would have can never be written "would of." However, the latter does exist: when the present conditional would is followed by an expression that begins with of.
She would, of course, live with me.
Past: She would, of course, have lived with me.
I ask no more of you than I would of myself.
Past: I asked no more of you than I would’ve of myself.
The Bottom Line
The erroneous phrase "would of" is probably due to the very similar pronunciation of would’ve. I would’ve told you this sooner, but I needed to save something for the bottom line.