Some answers are a bit misleading - especially those quoting the *Scientific American* article. You can only get the mass of the primary object from simple orbital mechanics. So you can't get Ganymede's mass simply from observing the radius and period of its orbit around Jupiter (it's a pretty good way to get *Jupiter's* mass - but that's not the point). Any object at the radius of Ganymede would orbit Jupiter in the same period - regardless of its mass.

For a sphere of given size, the gravitational field at the surface is depends on the density so that:

$$
\rho = \frac{3g}{4\pi G r}
$$

So if you want Earth-gravity on a planet the size of Ganymede, you'd need to make it out of material with a density of about $15\space g/cm^3$.

This is pretty dense - about three times Earth's density. However, if Ganymede is mostly made of some very dense elements like Tungsten or Uranium (as mentioned by @Ruadhan) it would work.