Machine learning is an actively growing field. There are many learning resources available that cover both the fundamental concepts of machine learning, deep learning in particular, and specific technologies like TensorFlow. This page provides a few suggestions for getting up to speed on machine learning, so that you can start using Cloud Machine Learning Engine to tackle your own machine learning problems in the cloud.
You can find a great introduction to some of the core concepts and basic techniques of machine learning in the Google Developers series, Machine Learning Recipes with Josh Gordon, on YouTube.
For a more in-depth treatment of the basics that's still very approachable to a newcomer, the course simply called Machine Learning offered by Udacity is worth a look.
A great way to learn how neural networks work is to build one interactively and watch as it trains its model in the TensorFlow Playground.
Once you have covered some of the basics, you can start making models of your own with TensorFlow's high-level API, tf.learn.
One of the biggest challenges in machine learning is finding good data to use as the basis of your model. That is, finding data that you can use to answer new and unique questions. As you are learning about machine learning, a good source of datasets is Kaggle.