We all use this construct, even if we don't know what it's called. Mostly it's used for something that didn't actually happen in the past. For example: If I'd known you had a Kindle, I'd have recommended some books. This sentence implies that I didn't know you had a Kindle, and because I didn't know, I didn't recommend any books. When I know someone has a Kindle, I recommend books.
It's like an If...then statement: If this, then that. Let's ditch those contractions to see what's under the covers.
If I had known you had a Kindle,
This part is supposed to be in the past perfect tense (had known)
(then) I would have recommended some books.
Here's where the conditional perfect goes.
This is where many people err.
They improperly use the conditional perfect in both the If and the Then parts. For example,
If I would have known you had a Kindle, I would have recommended some books.
The "rule" is that the conditional perfect can only be in the Then section.
More examples of proper usage:
correct: If I had gotten paid on Friday, we could have gone out to dinner.
incorrect: If I would have gotten paid on Friday, we could have gone out to dinner.
correct: If he had proposed, she would have said yes.
incorrect: If he would have proposed, she would have said yes.
And please, whatever you do, don't type would of. It does sound a lot like the would + have contraction, would've, but it's not proper English.