After the dragons hatch from the eggs Daenerys places on Khal Drogo's funeral pyre, a pint-size Drogon is the one who climbs onto her shoulder and unleashes a fearsome scream. Drogon is Dany's personal mount (the one she chooses to always ride) and named after the late Khal Drogo. Even if Daenerys is not riding on his back, he's easily distinguished by his black and red scales, as well as his more pronounced red wings, which are also streaked with black coloring.
Drogon is the most visible of the three dragons by far since he regularly accompanies Dany wherever she goes (with the exception of that time he straight up ditches her in seasons four and five). In season seven, he appears in "The Spoils of Where," where Daenerys flies into battle against the Lannisters on Drogon's back, and he gets shot in the wing by a giant spear. He's not dead, but we imagine he's not doing so hot at the moment. Most recently he appears in the season eight premiere episode, "Winterfell," spying on Jon and Daenerys's date.