If Yosemite is free, why do I have to verify billing info? I am unable to upgrade to Yosemite because when I press the "Free" button it takes me to  a page where I must verify my billing info., then when I press done, it gives me "your payment method was declined" !!

Since it is free, why do I have to verify my billing info ?
and if my account is verified why is it saying declined, does it try to take money out of my account ?
and how then to install the new OS ?

Note: my current OS  version is 10.9.5
The verification is for your Apple ID for purchases. You can either set the payment option to none if you're from the US or add a credit card to it. This eases the payment option if you plan to buy apps from the store later.

But in the case of downloading Yosemite, You will not be charged for anything.