The First Era began with the founding of the Cameron Dynasty in Valenwood, altho I don't know if someone "declared" the beginning of a new era because of that or if it that was done later because it was a major known event and subsequent historical record-keeping made it possible and easy to start counting there and date later events accordingly.
The Second Era began when rule of the Second Empire passed to the Akaviri Potentate after the assassination of Emperor Reman III and his heir. The new era was proclaimed by the Potentate.
The Third Era began by the declaration of Tiber Septim after he succeeded in bringing all the provinces of Tamriel under the rule of the Third Empire.
Please note that this is not so much a demonstration of my Elder Scrolls knowledge as my knowledge of where to look stuff up.
