I have discovered two shouts in my adventuring so far, Ice Form and Slow Time. I've also killed 4 dragons and absorbed their souls. For some reason I am not learning the shouts correctly. I was able to use Unrelenting Force after killing the first dragon, and I was able to use the shout the Greybeards taught me. But despite having killed dragons and absorbed their souls, I can't use Ice Form or Slow Time. Do I need to absorb more souls for this to happen, or are there specific dragons whose souls will let me use each shout? Or is my game hopelessly bugged?

You have to spend them by going in the menu and pressing the "unlock" button.

ya if the shout is greyed out then it is not "unlocked" for use because u havent spent a dragon soul on it. whatever platform u play on at the bottom of the screen in the left hand corner there is an option to "unlock", it is next to the favorite and the equip options, opposite the Dragon Souls # you have. Hope this helps! Good luck!

Oops I guess I missed that, thanks.

Go to your Magic Screen- go down to shouts- highlight the one you want to unlock- unlock the shout using one of the souls (press X if on X-box)- enjoy!