How do you measure the distance from earth to a nebula?

There are actually a number of different techniques that are used to estimate the distances of various astronomical objects. You can study the spectrum of the light (or any electromagnetic emission) from that object, and determine how much of a Doppler red shift there is (it's almost always a red shift, very few objects are approaching the Earth) and since the general rate of expansion of the universe is known, we can determine from the size of the red shift how far away something is. If the nebula is associated with a Cepheid variable star, then from the rate of variation and the brightness of the star, we have another clue. And, if we observe the nebula at two different seasons of the year, when the Earth is at opposite sides of the solar system, we may be able to get some parallax for a geometrical calculation, but that depends upon how far away the nebula is; if it is extremely far away, we don't have enough parallax to do it.