Simply use a standard sigmoid/logistic activation function on the output neuron. sigmoid(x) > 0 forall real-valued x so that should do what you want.
By default, many neural network libraries will use either linear or symmetric sigmoid outputs (which can go negative).
Just note that it takes longer to train networks with a standard sigmoid output function. It's usually better in practice to let the values go negative and instead transform the outputs from the network into the range [0,1] after the fact (shift up by the minimum, divide by the range (aka max-min)).