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.
It takes a lot of practice to do it properly. You can find basic instructions all over the Web (try Google). A recently-published (and inexpensive) book by R. Avraham Reit entitled Teka Beshofar has many useful tips and much helpful information.