Getting a sufficiently uniform field to really observe 1H line width is quite a challenge (I doubt a hard drive magnet will be anywhere near good enough), but it's nonetheless quite achievable.
Here's the classic citation (I have a PDF copy handy):
Bloembergen, Purcell, Pound; Relaxation Effects in Nuclear Magnetic Resonance Absorption, Phys. Rev., 73, no. 7 (1948)
The authors (and others) have related articles earlier and later. One (I don't happen to remember what, but I believe it was also in Phys. Rev. a few years before this) even shows the splitting effects of the different hydrogens in ethanol, founding the study of chemical NMR.
The apparatus is pretty primitive, though achieving field uniformity requires precision, adjustment, and a lot of poking around. They used an impedance bridge approach, which can be nulled in both amplitude and phase, detecting the NMR signal as an imbalance in the "antenna" leg of the bridge. Signal source was a radio signal generator (it will have to be stable in the Hz/minute range, so a good quality LC oscillator is needed, or even crystal controlled). Signal amplitude was amplified and detected with a radio receiver, and read out on an oscilloscope. Sweep was done magnetically, with a small variable DC bias coil driven by an amplifier and low frequency oscillator. (Of course, frequency swept sources weren't so practical back in the day, so they didn't bother with that method.)
These days, usual process is to zap the nuclei with an RF burst (in-plane from the same coil, or out-of-plane from a perpendicular coil), and measure the FID (free induction decay) with an RF downconverter, DAQ and FFT. The signal bandwidth is <100Hz, so a quite aggressive downconversion can be used (like going from FID at 30.000MHz down to audio frequency with a 29.998 MHz local oscillator and mixer). Multiple channels (X-Y-Z coils) can be used to gather more information about precession and relaxation time.
Tim