Go to Kaggle and enter a data competition. It is super, super easy to start (usually you just have to submit a solution which is a bunch of 1's and 0's) but to win, or even increase your rank, requires learning of real, practical data skills. I believe some companies even do recruiting through kaggle competitions.

If you go this route, download the scipy superpack which includes scikit-learn. You can spend five minutes reading about e.g., Naive Bayes classifiers, and then five minutes later you can be checking out how it works on your data!