I have killed many a dragon so far in the game. I have also learned new shouts but they aren't "powered" up yet by absorbing a dragon soul.

How does this work? I thought that just by killing a dragon I would be able to use a new shout. Is my thinking wrong or am I not doing something right.

Thanks in advance.

It's not automatic - you have to select the shout in the shout menu then hit the appropriate key (X, square or R, depending on system) to spend a soul to unlock the word.

Rinse and repeat for each locked word

You use souls to unlock words. But souls don't give you words of power.