Theory:
The verb HAVE can have three functions:
It can be a normal verb - I HAVE a dog.
It can be a modal verb - I HAVE TO go.
It can be an auxilliary verb - I would HAVE called you.
When used as a modal verb, it changes its V to an F, and the word TO changes to the SCHWA sound:
I have to go = I HAF ta GO.
You have to pay = You HAF ta PAY.
When it's used as an auxiliary it's often contracted, and when it comes after a consonant sound it's pronounced uV. So,
I would HAVE called. i'd HAVE called. I'd've called.
This pronunciation is very common in conditional sentences, but it's not the only time you'll hear it.
I would've gone.
We could've finished earlier.
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