Go here...
http://actofvalor.com/bf3/ ...and watch the video. At the end, it will give you a code to get the dog tags. Click on the FAQ to figure out how to enter the code.
EDIT: Here's the instructions:
How do I redeem the dog tags? (PlayStation 3 users)
Watch the video and follow the link. Log in with the EA/Origin account that you use to play Battlefield 3, and a voucher code will be displayed on the confirmation page. Write this code down, then log into PlayStation Network, then select "Account Management" and "Redeem Codes". Enter your voucher code and follow the instructions.
How do I redeem the dog tags? (Xbox 360 and PC users)
Watch the video and follow the link. Log in with the EA/Origin account that you use to play Battlefield 3, and if no error appears on the confirmation page, the dog tags should be available in the game the next time you start it.