I believe we have seen pretty close to the beginning of time, so the distance in light years is equal to that time.
Remember, since light takes time to travel, you are looking into the past whenever you look at something. For something close to you it's less than a nanosecond, but in space, that time matters.
We measure the distance by measuring the intensity of the background radiation from the big bang, which dissipates in a well-known manner. By measuring the level of this radiation, we know how long ago the thing we are looking at happened, and thus know how far away from us it is by multiplying that time by the speed of light (actually, the distance in light years is equal to the time because of the way the units are defined).