What steps should a person take to develop initial competence in sounding the shofar?
Are there online or other training materials available? Any tips specifically for a neophyte?
I don't know the best way to learn how to blow shofar but I can tell you how I learned.
Firstly, I was told that as a child that the main thing is to NOT BLOW into the shofar. That is, the shofar is not a baloon, and you do not want to blow into it directly. You want to shape your lips and allow the air to pass through them, but you do not want to blow directly. A good comparison instrument (that is easy to get hold of ) is a Kazoo. (I know nothing about other horns or wind instruments so can't compare)
After that initial lesson, it was just a matter of practice and reading up on the various halachot of blowing shofar.
I, too, learned like avi with an initial lesson and then on my own. I'd like to add some suggestions to his answer.
One important thing to know is that there are shofars that are easier than others to blow. I suggest you find someone who can lend, or recommend, an easy shofar to you. Then the next step is to learn a basic way to get to produce a solid sound (a sound that is not simply the "ffffffff" of when you blow into it). Afterwards you practice on your own.
I would also say that when you have a basic grasp of the fundamentals you can ask a Rabbi to help you refine your technique according to his tradition. Sephardic, Ashkenazi and Italian Jews have different traditions that prescribe how to blow the various sounds.