I think the easiest and cheapest way to get into animated movies, is to use Blender. You can create models and animations but also render them for a full movie. Actually they made a movie completely in blender with a big bunny ( don't know the name right now)
If you want to do it on your own, you have to write an engine (Rasterizer like UE4, Unity etc. or Raytracer like 3D Studio Max, Blender etc.) and store keyframes on a timeline with matrices (position, rotation, scale) for every object/objectpart in your scene. Now you can interpolate between those frames, render and store them as a video.