If we assume that this is a harmonic sound (which is a good enough assumption for pianos) and that this is a spectrum of only one note being played, then the fundamental frequency n will be the highest frequency such that F1 = a1n, F2 = a2n, F3 = a3n, ..., where a1, a2, a3, ... are all positive integers. (In other words, n is the greatest common divisor of F1, F2, F3, ...)
For example, if we were given a plot with F1 = 200Hz, F2 = 300Hz, F3 = 500Hz, F4 = 600Hz, then we could say pretty confidently that the fundamental is 100Hz, since the peaks are at 2*100, 3*100, 5*100, 6*100.
One way to make a guess at n is to look at the difference between two peaks (e.g. 600Hz-500Hz = 100Hz). There's a pretty good chance that this will be the fundamental, but you have to go back and verify that your guess is right... It's possible for tones to be missing harmonics (The example I gave here is missing the 400Hz harmonic, so you might guess that the fundamental is 200Hz, which is not right).
(And if you were given a plot with F1 = 201Hz, F2 = 297Hz, F3 = 499Hz, F4 = 602Hz, you would conclude that the fundamental is still 100Hz but there's some measurement error, or the tone isn't quite perfectly harmonic... Most of these plots are not precise enough for tuning)