Intro
Ok, this is from personal experience at trying to get some store bought content to work with the steam version WITHOUT using Origin.
NOTE: you do need a log in for the Sims 3 and for the Sims 3 store, make sure you have one AND are logged in before attempting any of this.
Frankly speaking, there are two methods to do this:
For the Launcher (if from disk)
This method is if you want to install it through the launcher.
Step 1:
Insert the disk into the disk drive and open it to show the folders on the disk.
Step 2:
Find the add-on (it should have Custom Content in the type column and will usually be inside a folder, locations vary).
Step 3:
Run the file as custom content.
Step 4:
At this point the launcher will start and you need to type in the 16 digit Serial Code, which will start the install.
Through the Sims 3 website
For this method all you need in your log in and the Serial Code.
Step 1:
Open store.thesims3.com
Step 2:
Go to My Page in the top bar, move down the drop down to My Account and select Redeem A Code.
Step 3:
Type in the Serial Code and register it to your account.
Step 4:
Go to Store in the top bar, move down the drop down to My Store Account and select Purchase History.
Step 5:
Find your newly added item and hit download, which will start the download process.
Other Notes
DISCLAIMER: This is from my own personal experience and may not work for every addon or bundle purchased from a store.
If you do all this, I would also suggest registering your game plus the add-ons as you can get around 1000 sims points to spend in the store plus several free items. Registering in the store also allows you to use Origin (uugh) to play the game with all the add-ons that you have.