Using the formulas in the tutorial and in my notes, write code that will adjust a model given a starting model and an observation sequence. Then start off with a random model and see how easily it converges to the correct model. You'll need some difference measure between models. I suggest using the sum of the squares of all the model parameters.
The issue of how to test the model that results from training is not an easy one. See my HMM notes for a discussion.