What are some methodologies for performing feature selection for simple feed-forward neural networks?
I usually try to do the following process, I don't know whether it has name or not:


Try to find features which an expert can say what the label is without hesitating. 
Plot correlation matrix for your sample to investigate whether each feature has correlation with others or not. I do this process whenever the input features are so much. Then try to reduce the correlated features or try to apply PCA. Consider the point that PCA alone does not care about the labels, so it may find principal components that your data would be so difficult to be separated but not necessarily.