So I would consider myself a biginer in After Effects.
The reason yours looks so bad is that this person is using expressions driven by sliders for various properties. This is sophisticated AE animation, and well beyond a beginner's capabilities. Even if someone were to give you detailed, step-by-step instructions to recreate it, you wouldn't understand them.
You really need to start learning AE here. Seriously. There are no shortcuts. No matter how much you want to run, you can't do it before you learn how to walk.
Smooth animation for something like this either requires a bunch of frames, some sophisticated transforming or some animated shapes. You can't get it with just 3 frames. The blinking eye is not just one layer with the face and eye. It's a layer for the eye, a layer for he eyeball, a layer for the eyelid and probably involves some scaling of that layer. Rigging artwork for cell type animation in AE requires careful planning and many layers. Make sure you're well versed in the basics Dave pointed you to and then move on to looking for tutorials on rigging for character animation in AE. If you have a few dollars try a one or two month subscription to Lynda.com or Total Training. They have great tutorials presented in a way that will teach you more about AE in less time than poking around the web for specific tutorials.