Getting started with animation accelartion? My animations look completely robotic and lack any acceleration, how can I solve this? 

I saw something similar using curve graphs, but I'm not that advanced yet, if someone could give me a get started tutorial.

I knew blender well just not the graph stuff.
Perhaps this will help you get the acceleration you want:

Blender Basic Animation - Using the Graph Editor and Interpolation Modes

https://www.youtube.com/watch?v=R9gCHhJOjlQ

In this intro, inascott888 positions a cube and keyframes location at the start frame, he then goes to the end frame, repositions the cube and keyframes location there. In the graph editor window, he then uses the bezier handles to change the shape of the transition curve, and shows how this can be used to effect acceleration of the cube (when the animation is played back), that is by making a very slow start, but increasingly steep curve up.