This may seem simplistic but here's my basic understanding of it:
Number of peaks: Each distinct group of hydrogens will produce a peak
Splitting of peaks: The number of smaller peaks each peak splits into will be based on the n+1 rule, where n is the number of hydrogens on the neighboring carbon(s) that are 3 bonds away.
Area under a peak: Basically the integral of a peak will be proportional to the number of hydrogens of that type.
So...CH3-CH2-CH3 would produce two peaks (one for CH3 groups, one for CH2 group). The CH3 peak would be a triplet because there are two hydrogens neighboring. The CH2 peak would be a septet. The ratio of the area under the CH3 peak to that under the CH2 peak would be 3:1.
Hope that answered the question!