Basically, to tame a Hesperornis, you have to kill Coelacanth and drag their corpses in front of it, bigger ones seem to give more Taming Process(further testing needed). Once you tamed it, drag more fish corpses to it and let it eat, after a certain amount of fish, it will then lay wether a golden egg or a hesperornis egg. The hesperornis egg can be cooked into oil, the golden egg, if eaten, gives your dinos 500% experience for I think 10 minutes, but will give yourself only 10%. The golden egg is also used to cook kentro kibble which is needed to kibble tame the epic yutyrannus.

More Hesperornis Taming & KO Tips