Measuring time and distance in space When reading through articles about discovering gravitational waves, I got basic understanding of events that happened. But one thing wasn't clear for me. They say that two black holes collided 1.3 billion years ago. 

My question is, how can we know, that this collision happened 1.3 billion years ago?
A model is fitted to the signal that depends on various input parameters. The input of the model that fits the signal best is then considered the "most favored" model, while the input of models that fit better than a given threshold are used to infer confidence intervals on the various parameters.

The model has to simultaneously reproduce as well as possible the frequency and the amplitude of the signal. Among the input parameters are the black hole masses ($36_{-4}^{+5}\,M_\odot$ and $29_{-4}^{+4}\,M_\odot$ ) and (luminosity) distance ($410_{-180}^{+160}\,\mathrm{Mpc}$), corresponding to a light travel time of roughly 1.3 Gyr, depending on the assumed cosmological density parameters (they used those of Planck 2015).