What makes Google Google? Arguably it is machine intelligence, along with a vast sea of data to apply it to. While you may never have as much data to process as Google does, you can use the very same machine learning and neural network library as Google. That library, TensorFlow, was developed by the Google Brain team over the past several years and released to open source in November 2015.
Most developers should start learning TensorFlow by checking out its code repository and model repository. The next step is to install TensorFlow and validate your installation, while reading the introductory materials and going through at least one MNIST tutorial, which shows you ways to recognize handwritten characters. Then by all means go through the other tutorials, which show you the basic mechanics of TensorFlow and
tf.contrib.learn, a high-level API for TensorFlow. Then, depending on your interests, you can dive into image processing, language and sequence processing, and non-machine-learning applications (Mandelbrot set and a PDE simulation).