How do I find out when are the Credit Cards billing cycle dates?

Typically it begins upon card activation or successful application, I believe.

One way to avoid late fees and headaches wondering if you made payment for your credit card bill is... to call your credit card provider/bank to align the billing dates.

For example, I have called AMEX to align the billing cycles of both my cards on the same day. Yes there will be some adjustments for a month or so until the cycles align.

So be prepared to pay higher than usual credit card bills(as transactions will shift) during that period.

Call up customer service officer hotline of your bank credit card provider. They know the best and the conversation is recorded. So anything you can quote his or her name as evidence.