I wrote an article titled “How to Reuse Neural Network Models” in the September 2015 issue of Visual Studio Magazine. See https://visualstudiomagazine.com/articles/2015/09/01/how-to-reuse-neural-network-models.aspx.
A neural network can be thought of as a complicated math function that makes predictions. The process of finding the numeric constants (called weights) that define a neural network is called training the model. For example, a neural network with 5 input predictor variables, 10 hidden processing nodes, and 3 output nodes has (5 * 10) + 10 + (10 * 3) + 3 = 93 weight values that must be determined. This is done by using a set of training data that has known input values with known, correct output values, and then trying different values of the weights until the computed output values closely match the correct output values.
Training a neural network can take a long time so it makes sense to save the weight values (and other information such as the number of hidden nodes). I describe exactly how to do this in the Visual Studio Live article.