How do you calculate a dividend payment with the use of the retained earnings data? Thanks!

Only net income (loss) and dividends declared are in retained earnings. You will always have the first. If the second exists, that would be a debit out of that account.

However, dividends declared may or may not be the same as dividend payment. If not, the payment isn't in retained earnings.

The trouble with questions like this is that we're getting them out of context, don't know what you're working on, or what kind of info the problem has available. It would help to have that info.

I am putting together a statement of cash flow. Dividends are not given and my professor said to infer from the dividend payment from retained earnings (which is given/stated on the balance sheet).

Infer it from the retained earnings, magically, with no explanation? How nice.

So cash flows -- that would be another adjustment using the dividend payable account. When dividends are declared and not paid, it's put into dividends payable. Then when it's paid, it's taken back out. So if the balance in that account has changed, that means something is different from the amount declared.

The short-cut is just making this adjustment: if the balance increases, subtract it from the declared amount, and if it decreases, add it to the declared amount. That'll get you the amount actually paid for the sake of cash flow.