This is what I do. I don't know if it's the right way of doing it, but it extracts my sims fine and my game hasn't imploded yet so...
1. Make sure you're not running
The Sims 2 or
Bodyshop. If your computer isn't good at handling multiple programs at once then make sure you're not running any other programs.
2. Run
SimPE and wait for it to load (it takes a long time for me). Make sure it is the version for your latest Expansion Pack.
3. Once the program has loaded, go to
File>>Open...4. Once the
Open Package window pops up, you'll need to go to
My Documents>>EA Games>>The Sims 2>>Neighborhoods.
5. Select the Neighborhood you want to extract your sim(s) from. For me, it was
N174, my storyhood.
6. In the
neighbourhood folder, find that file that will be named something like :
N174_Neighborhood. This is the file you want to open. Do so. It again will take some time to load.
7. Once it is fully loaded, go to
Tools>>Neighborhood>>Sim Surgery... It will take some time to load.
8. Once it is loaded, you will need to browse down the left side column and find the sim you want to extract. The sims are sorted alphabetically by first name.
9. Once you have found your sim, click on him/her and under the blank square on the
Patient Sim panel, click
use. Your sim's face will appear in the blank box normally, but if it doesn't, not to worry - their name should still appear in the panel, along with their lifestage and gender.
10. When you have done this, click
Export. A window will pop up prompting you to save. Don't bother to change your sim's file name and just click
Save. Your sim is now exported! But you're not done yet.
--- Rule of thumb: make sure you extract all the sims you want once you have SimPe booted up. It takes so long to load, it's something I personally hate to do on a regular basis so I only load it once in a while, then bulk extract ---
11. Once you are finished, exit
SimPE. Now load
The Sims 2 Bodyshop, the one your latest EP is equipped with. Again, wait for it to load.
12. Once it is booted up, you need to go into the Sim bin, find the sims you've extracted (for me, the extracted sims are always near the end of the custom saved sims, near the premade Maxis binned sims) and
clone them,
saving the clone,
before deleting the original extracted sim. This is a precautionary measure (but one you should
ALWAYS take) so that the sim you've extracted doesn't have a chance to corrupt your game. If you use a clone of the extracted sim, any chance of this is eliminated.
Now you're done! Package your extracted sim for download or back up, go in your game and see him/her in the CAS sim bin, do whatever you want really. I hope this helps.
Might update with images in a while, because I just extracted some sims there so I could type it up precisely and took printscreens so I could remember what I'd done. 
