Neural Network Training

I'm trying to learn about neural networks and AIs. So far, I think I'm understanding most everything but I am having trouble figuring out one thing. How do I teach a neural network(feedforward network)? For example, let's say I have a three layer network with 2 perceptrons in the input layer, 4 in the hidden layer, and 1 in the output layer, and I know the desired output of the output layer only, how do I adjust the weights of all of the other layers? Do I need to know the desired output for each individual neuron (which I hope I don't because that would get annoying quick with larger nets) or is it possible to do it off of only knowing the final desired output(s)?
You only need to know the desired output of the output layer. A common method to train feedforward neural networks is back-propagation algorithm.
All i know so far is that it is described using graph theory and matrix transformations, finding the shortest path
Thanks for the replies. I'm going to check out those methods and see what I can do with them.
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