Actually there is no "far" for the expansion of the Universe. According to scientific measurements and experiments, the Universe is constantly expanding, and it is very complicated to explain and understand this process. The Universe has not a boundary where it all stops, and there is no "outside" the Universe. The Universe is effectively curved round on itself, so if you keep going far enough you would get back to where you started.
It was in 1929 that Edwin Hubble, an astronomer at Caltech, discovered that the universe is expanding. Hubble used large and accurate telescopes that were able to measure the intensity of light of distant galaxies. Hubble combined his own measurements of galaxy distances with Vesto Slipher's measurements of the intensity of light shifts to conclude that the Universe was expanding.
Today we know that the galaxies astronomers see in all directions are moving away from the Earth, and there is the Hubble's law that describes the Expanding Universe.
You can just say that the Universe will expand as far as human beings will exist on Earth.
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