I would say that a good example for starting in this field would be to implement something like Tf-Idf [0] for identifying keywords on a set of documents. I don't know where one can find current datasets for this, but I made WikiCorpusExtractor [1] to build sets of documents from the Wikipedia.
The only thing one really needs is to count the frequency of words in each document and do very simple math. Tf-Idf is still very relevant today and provides you with a very good idea on how statistics is used on text-mining.