The thing is that SkeletonAnimation is the thing that initializes (and kinda "owns" the Spine.Skeleton in the first place, so that's were you do need to go to find the Skeleton you want).
If this script is attached directly on the same GameObject that has the SkeletonAnimation component:
void Start() {
skeleton = GetComponent<SkeletonAnimation>().skeleton;
}
SkeletonAnimation also has a member called state that you might find useful to keep a reference to. It's a Spine.AnimationState and it's what you use to play animations and things.
Going forward, here are some useful classes you'll find helpful to go over the code of. At the very least, check their member fields and properties to know where you can find things and how they're pieced together. There's some Unity specific stuff in SkeletonAnimation (and its base class, SkeletonComponent) that you won't find in the official docs:
SkeletonComponent
SkeletonAnimation
Skeleton
SkeletonData
AnimationState
Bone
Good luck with learning C#! It's a very neat language. Keep at it!