I can't detect that anything happens when my character abosrbs a Dragon soul after killing the Dragon.
There are several greyed out shouts in the magic menu, and two that are usable. None of them change when he absorbs a dragon soul.

http://www.uesp.net/wiki/Skyrim:Dragon_Soul#Achievements states that

It seems that I'm missing out on the second part.

Upon rereading that page, I found the following:

So I guess there's some info at the bottom of the screen telling me how to unlock a shout (I'm using PS3).
Correct?

How do I know how many souls I have available?

uh, I dont know about ps3 but on the xbox you go to shouts in the magic menu, highlight any shouts you dont have unlocked and press x to spend a dragon soul. at the bottom of the screen it should say how many dragon souls you have.... is this a joke ? If not hope this helps

I use an xbox controller on my PC, and it's the X button that unlocks the word using a dragon soul. It will ask for confirmation. Once that word is unlocked, you can select it under Shouts in the Magic menu. On my controller shouts are assigned to the right button, above the "left" trigger switch.

This is not a joke. I guess the lesson is to scan the bottom (or the whole) of the screen every time I wonder why I can't do something in the PS3.
I'll check it out when I get home. Thanks.

You know, plenty of peole, myself included, have asked this same question. You get tooltip messages the first time you go to use Alchemy, Smithing, Enchanting, even when your health/magick/stamina run low. Why not unlocking shouts?

you can only perform the unlock when you progress the main quest, meet up the guru of shout, who will teach you few extra yelling.

Yes, I had the same issue at first. I tried highlighting the unlocked shout with a mouseclick instead of with the arrow keys or however you're actually supposed to do this. And I had remapped my keybindings, so I didn't exactly know which button the game wanted me to press. Because for some reason, Beth didn't manage to update the hint messages according to the actual keybindings.

I'll definitely check this out when I get home.
Lytha, your avatar rocks

For the record, it's all there on the PS3 at the bottom of the screen, hidden in plain sight.
How to unlock, how many souls I have and more.

I think it throws people off because the first shout is unlocked automatically so you can shout at the soldier after the battle who's tell you that you're dragonborn. I've seen this question many times too.