FOR 20 DIGIT CONTENT KEYS:

If you have not done so already, create your free Origin/EA account on http://www.origin.com.
Log in to the Sims 3 community website using your Origin email and password. If you are logging in for the first time, use your provided key for the Sims 3 base game during the registration process.
To redeem the games on your Sims 3 account select "My Page" -> "My Account" -> "Register a Game"
Enter your 20-character key for The Sims 3, Late Night Expansion, or High End Loft Stuff. (note, if you entered the The Sims 3 base game code in step 2, you don’t need to re-enter it here)
That's it! The Games will automatically be added to your Origin account, and can be accessed and downloaded through the Origin client.

The Sims 3 and all of the DLC will be available for both Windows and Mac.
Every The Sims 3 add-on pack can be redeemed through the Sims 3 community site. To redeem follow these steps:

Log in to the Sims 3 community website using your Origin email and password: http://www.thesims3.com/
Under the "My Page" menu section at the top of the page, scroll down to "My Account" and select the "Redeem A Code" option under the sub-menu.
Click on "Redeem a Code"
Type in your provided "Sims 3 Date Night DLC Community Key" from your unique download page and click "Redeem".
Click on the link for your "Purchase History" which should be visible after typing in your code. You can also access it under "Store" > "My Store Account" > "Purchase History" from the top of the page.
Click on the "Download" link under the icon. This will open your Sims 3 launcher and begin downloading the content through the launcher.
Once finished downloading, click on the "Install" button below.
That's it! You will now have additional clothing and content added in to your Sims 3 game!

 FOR 16 DIGIT KEYS:
Please login to your Origin Account and redeem your keys under this link