Training a Neural Network on MIDI data with Magenta and Python involves installing the Magenta library, creating a dataset of music files in MIDI format, converting them into "NoteSequences" that are easier to work with for training, creating "SequenceExamples" to be fed to the model during training and evaluation. Once trained, the model can generate new polyphonic tracks using the `polyphony_rnn_generate` command, allowing users to experiment with different parameters and hyperparameters to create unique music outputs. After generating music, users can bundle the model into a portable file for easy sharing or use on other devices.