It's actually super refreshing learning that even programming masters like Carmack are just now learning NNs and watching Youtube Stanford classes like the rest of us. These are actual people, not gods :) Everybody poops!
backprop is a very simple algorithm, nothing to fear there. The problems are to calculate the derivates if you want to be flexible building your model. But for feedforward networks with sigmoid activation, the equations to update the weights are a joke.
You won't regret. One of the best explanation of backprop on the internet.
But I meant, if you see the equations and the steps without understanding completely the insights, it is a joke of an algorithm. It just does some multiplications and applies the new gradients, move to the previous layer and repeat.
So it's probably as simple as
newWeight = oldWeight +/- (stepValue * someFactor)