You find some randomly in the wild but best way is to tame the Dino you want. A male and female pair will boost the rate and an oviraptor will boost it even more
Well, the only reason I was wondering is because I was mating my Megaloceros and the baby requested terror bird eggs... and I was like where am I gonna find those, lol.
You would have to tame a bunch of terror birds (3-4 females and 1-2 males) and let them lay a bunch of eggs. Collect them up and refrigerate. Build a garden and preserving bins of meat and prime jerky.
Use recipe to make kibble. At first it seems like a lot of work but after time you get a bunch of dinos and stuff just comes together.
Use SA companion app on phone to have almost all information about ark.
Since you're on single player you can turn down the egg lay interval and you'll only need 1 female of each dino. Cheaty yes but might as well have fun with tweaks since you can lol
While possible to find some in the wild, females will drop unfertalized eggs by themselves as a tame. These are easier to get, and don't incur the wrath of parents. They drop more often when a male is present.
For fertilized eggs(not needed for kibble, but can be used), you need to set them to wander and begin mating