While still in CAS, before accepting the family, click on the three dot ("...") button at the bottom of your Sim's portrait thumbnail. That'll bring up a little menu that includes the "share" button. You can also save your Sim to your Sim library from there, if you want to do that as well.
Alternatively, if you already have a Sim in a family in game that you want to use as an avatar, you can have them use "Change Appearance" on a mirror or "Plan Outfit" on a dresser to load them into CAS mode. From there, you can do the same thing, with the three dot button next to their portrait.
From there, all you have to do is upload the Sim to your "My Creations" page from the Uploads panel in the Sims 3 Launcher.
Comments
While still in CAS, before accepting the family, click on the three dot ("...") button at the bottom of your Sim's portrait thumbnail. That'll bring up a little menu that includes the "share" button. You can also save your Sim to your Sim library from there, if you want to do that as well.
Alternatively, if you already have a Sim in a family in game that you want to use as an avatar, you can have them use "Change Appearance" on a mirror or "Plan Outfit" on a dresser to load them into CAS mode. From there, you can do the same thing, with the three dot button next to their portrait.
From there, all you have to do is upload the Sim to your "My Creations" page from the Uploads panel in the Sims 3 Launcher.
Hope that helps.