Soul gems are for something else, and I have no idea how you use them.
The dragon souls are absorbed by you automatically after you kill a dragon (I guess you have to stand near the body when it does the swirly lights thing), and you can 'spend' them on activating a word. Getting two or three words from a combination (each shout has three parts, each in turn making it more powerful) is useful, but then so is having a variety of different types of shout. I think I have four active shouts at the moment - disarm (doesn't seem to work for me), fire breathe (this is quite effective), some sort of shout that makes enemies run away... and another one I can't remember.
Dragons spawn 'randomly' and 'rarely', but they are also usually guarding the shout stones in the world. I haven't found a map (image) that shows where the words are found yet, but I've stumbled on several on my wanderings when I don't fast-travel.
My technique for killing them is to use the best arrows/bow I can get hold of, and then hiding in an arch or tunnel so I can peek out to shoot it then hide from it's breath in the tunnel.