In ANN modeling a graph having input nodes connected to one single output node is developed. Each connections to the output node will have its own weight assigned to it randomly.
At the output node all the weighted input nodes are summed up and activated or magnified with the help of Activation Functions.
The Activation Functions can be of many types like Step,Ramp,Hypertan,Sinusoidal,Sigmoidal etc.
After being activated the output is compared with the desired output(Supervised NN) or the median/mean or any other measures of a set of attributes(for making clusters;Unsupervised NN).
If the output from the model is satisfactory with the objective of the model, then the model is said to be learning and if not, the weightage of the connections are changed and the entire process is repeated.
This changing of the weightage is known as Training of the network and is conducted by various methods but mainly by Conjugate Gradient Descent, Back Propagation and/or Quick Propagation and/or by some special algorithms like Levenberg Marquadart.