How do we choose the activation function for each hidden node? I am new to neural networks. I would like to use them as a fitting or forecasting method.

A simple NN model that does not contain hidden layers, that is, the input nodes are directly connected to the outputs nodes, represents a linear model.  Nonlinearity begins to appear in an ANN model when we have hidden nodes, in which a nonlinear function is assigned to the hidden nodes, and using minimization their weights are determined.

How do we choose the non-linear activation function that should be assigned to each hidden neuron?
To know the form of your non-linear function,  firstly you should define the type of problem you are dealing with such as an image classification task. Secondly, pick the activation functions based on your task such as sigmoid, Tanh, ReLu, LeadyRelu, Softmax etc. Overall, your ANN performance mainly depends on the number of hidden layers (hidden units), selection of activation functions,  weight decay, momentum and dropout etc.