I want to calculate the amount of dividends declared and paid during the year by a company. What is the information needed (the formula)? Thanks

Based on what information? There isn't just a formula to figure dividends declared. We next some context here.

As morgaine said, there are many ways to come about this information.

One such way is to look at the retained earnings account (beg and end) and net income.

A simple short hand quick way to think about it would be:
Opening RE + Net Income – Dividends = Closing RE