How does one compute the band width of a signal in the time domain $x(t)$?
As far as I know there is no way to get $f_{max}$ and $f_{min}$ directly from time domain (zero crossing rate will not help if the signal has a non-zero DC offset for example) you need to look at the frequency domain.

If there is just one term, the smaller frequency is just $0$

Given a time signal and its sampling rate ($Fs$), you can take the discrete Fourier Transform to study its frequency spectrum. Unfortunately you cannot use this to decide your sampling rate if your initial sampling rate ($Fs$) is lesser than the 2$*$bandwidth (2$*$[highest frequency] if you are looking for perfect reconstruction) as you have already lost the data during initial sampling(look up aliasing for further reading). 

Bottom Line: You need to have an estimate in what frequency range your signal will lie so that you could sample it accordingly.