Essentially there are two ways to do this. The “old” way is to export your TensorFlow neural network into a protobuf file, then load up the TensorFlow interpreter in your iOS/Android app, feed it the neural net, and run the inference directly on device. The GitHub repo [0] has a good set of examples of what that looks like in practice.
The new, still experimental way is to compile your neural net into executable code with their XLA / tfcompile tool, and link that into your app. They are adding more docs on this on the TensorFlow website [1].
[0]: https://github.com/tensorflow/tensorflow/tree/master/tensorf...
[1]: https://www.tensorflow.org/versions/master/experimental/xla/...