Q: How can i get OS X installer which is a free app without having to enter a credit card?

In order to use an Apple ID without a credit card, you need to have set it up that way, meaning that you would have to have clicked on the download of the free app before actually setting up an ID.

At this point, you can either download a free app without being signed into the iTunes & App Store and then set up a new Apple ID to do the download, or you can put a credit card on your existing ID and once it is verified, you can then change it to "None":

Create an iTunes Store, App Store, or iBooks Store account without a credit card or other payment method - Apple Suppor…

If you do not see the "None" option after putting in the credit card:

Why can’t I select None when I edit my Apple ID payment information? - Apple Support

Cheers,

GB

Because that is how the App Store works.  An account requires a method of payment, whether you use it or not. 

If you don't have the option of setting None for the payment type, you can try using a "gift" card, or use a credit card, then try to set as None.

So when you created the Apple ID, did you do it via the method described (i.e., by downloading a free app prior to setting up the ID)? Have you downloaded anything on that ID prior to today?

Cheers,

GB

You are using the Mac App Store Application from your Mac's Apple Menu to download Yosemite, not some scam-artist's fake website that you found via a search engine? Just checking...

I have recently set up a work-related Apple ID recently and had no trouble selecting 'none' as the method of payment from the row of credit card possibilities.

C.