The graph shows three NMR/ON-spectra. To get the magnetic hyperfine field out of this spectrum, we first cool down towards the mK-range (to get nuclear orientation). Then we do an LTNO-experiment in an applied radiofrequency field. We repeat this LTNO-experiment until we found the frequency where the photons have enough energy to do the hyperfine transition (dip in the spectrum). At this frequency, the nucleus will have lost its anisotropy. This found frequency is proportional with the energy difference ∆E between the hyperfine transition. From this energy difference, we can deduce the hyperfine field B, because we know that this energy difference is proportional with the dot product between the nuclear magnetic momentum and the magnetic hyperfine field.
How we know the sign (what do you mean with sign?) of the hyperfine field is for me unclear.