I have a dataset (an array) and I need to find the periodicity in it. How should I proceed? Somebody said I can use FFT but I am not sure how will it give me the periodicity
You could use FFT because it will convert your data set from a value-space to a frequency-space.
This means that you will end up having a set of frequencies that composed will produce the initial input that you want to analyze. Then you can easily recognize which are the major contribuitions that are generated by specific frequencies and so you will understand how many periodicities there are and which are the most influential ones..
take a look here: http://local.wasp.uwa.edu.au/~pbourke/miscellaneous/dft/