The easiest way to determine if you have found an Eastern Cottonwood is from the leaf. As you can see, the leaf is rather large (typically in the 3 to 4 inch range, but sometimes up to 6 inches tall) with a distinct heart-shape.
This can be distinguished from other similar leaves (such as a Quaking Aspen) based on the size (the Cottonwood will be larger) and the texture of the trunk. The Aspen will have a smooth trunk, while a Cottonwood's trunk will be rougher and with deeper furrows, especially on larger trees.
The trunk can also be useful in identifying a tree in the winter, when the leaves are entirely off the tree.
Spring time will also allow the additional opportunity to identify the Cottonwood from the extensive amount of cotton the tree leaves behind. The cotton is predictably soft, white, and quite pervasive when the season is right.