Hi Darrius -
If your son used tax software, there should be an option for filling out the amendment, called a Form 1040X. The software should pull the numbers into the amendment for you.
If the original return was hand-prepared, you'll need to get a 1040X (go to IRS.gov and put 1040X in the search box). Then you'll transfer over the figures from the original return to the proper spaces on the 1040X from the original return, and then prepare the corrected information on a new form 1040. Attach the changed form(s) to the 1040X and send the whole package to the IRS (address depends on your location, see the instructions).
Either way you'll have to file this return by mail - amendments are not allowed via e-file. This will result in a long period of processing time. You'll probably need to file an extension for the return that you wish to claim him on, because the amendment won't likely be completely processed until after 4/15/2013 - and if you try to file before the amendment is processed your return (or at least the claim of him as a dependent) will be rejected.
Hope this helps -
Jim's got the right answer. One approach you could use to avoid paying fees and interest penalties is to file your return as if you couldn't claim your son as a dependent, pay the appropriate taxes, and once your son's 1040x is processed, file your own 1040x showing your son as a dependent.
The 1040x may sound like a pain in the backside, but I've filled out several of them in my time due to amended K-1s and the like, and it's not as bad as it sounds. Well, it's not bad for an IRS form, that is!