The usual workflow for creating animations for Unity games is to create them in a 3rd party 3d modeling program like Blender, Maya or 3dsMax and then import the animations into Unity as animation actions by importing the model. Unity can retarget animations via the Avatar component, so you don't necessarily need to do the animations with the same model which you are going to apply them to.
But if you still want to do it in Unity, then the new 3d rigging system might be what you want. It's basically a more advanced and flexible alternative to the build-in IK system provided by Unity. Although the basic IK system might do the job if you only want IK for hands, feet and gaze. The article I linked has an example script.
In either case you would create your IK targets as invisible game objects and then create actions using the Animation System which move those IK targets around.