Under iOS 7, there's a new, much easier way to teach Siri how to pronounce the names of your contacts. To check it out, invoke Siri by holding down the Home button until you hear the beeps, and then say something like "Learn how to pronounce [contact's name]":
Siri will ask you to say the first name correctly…
…and then it'll present you with three options for what it heard.
From that screen, you can press the play button beside each pronunciation to choose the best one, and you'll tap Select to confirm it afterward. If none of the options are a very good match, touch Tell Siri again to walk through the whole rigmarole from the beginning.
Then after you've picked the proper pronunciation of the first name, Siri'll ask you about the contact's last name. You'll follow the same process as above.
When you finish with the last name, you're all done!
In my testing, this has worked pretty darned well. The only hitch I've found is that if you ask Siri to learn to pronounce someone's last name only, it'll still make you go through the steps for the first name.
I guess I can give Siri a pass on that one. I hope my magnanimity will be rewarded when the robots take over, though.