Galactic Coordinate System and distance
You need three coordinates to represent a point in 3-dimensional space. Galactic coordinates are a 2-dimensional coordinate system on the surface of the abstract celestial sphere. Typically it is easier to measure position on the celestial sphere than it is to measure astronomical distances, so usually the systems are given in those terms. For 3D you need to supplement the Galactic coordinate system with distance as a separate coordinate, this is in fact the natural choice for a 3D spherical coordinate system.

Remember that the galactic coordinate system has its origin in the same place as equatorial coordinates (right ascension, declination), so the distance measurement is the same: you don't have to translate it relative to the Galactic Centre. To measure it, you use the usual techniques used to determine the cosmic distance ladder: parallaxes, standard candles (Cepheid variables, etc.), redshifts...