amplitude spectra, sin wave
i would recommend reading a richard lyonn's book about signal processing, it's very good for a begineer.
basically, first you usually do the filtering to remove higher frequency components (above 2*fs, where fs is sampling frequency). if you don't need (don't want) to remove higher frequencies, you proceed to sampling and then you perform dft of samples.
as somebody said, you get both positive and negative frequency components, because of dft periodicity. for most of purposes, you compute the absolute value of dft result (result * conj(result)), where conj is complex conjunction function.
and you have your spectrum...
for a sine, you should get a peak on frequency-amplitude graph exactly at the frequency of that particular sine. this is ideal case, and you will not get pure peek in practice because of many effects that are far beyond this simple explanation.
hope it helps
tahiti