The easiest way to do this is to connect your phone to a PC. Then you can open the phone like it's a USB drive and copy/cut and paste the folders from the phone to the SD card.
If you don't have access to a computer, you can do the same thing with a file browser app on the phone. The stock file browser on the S3 is called "My files" and the icon for it is a folder. Open that up and you'll see two choices "extSdCard" and "sdcard." The "extSdCard" is your actual SD card. The "sdcard" option is your internal memory (this is how Android reads the memory now, and it's understandably confusing for many people). So, if you want to move some folders from the internal memory to the SD card, tap "sdcard" after opening My Files. Next, tap Menu -> Move. You'll have check boxes next to all of the folders. Check off the folders you want to move (some of them might be inside other folders). After you've selected all of the ones you want to move, tap Done at the top right. Next, select "extSdCard," and navigate to where you want the folders moved to. When you're where you want the folders to be, tap Done at the top right. The will move any folders/files you've selected from the internal memory to the external SD card.
To automatically save pictures that you take to the SD card, open the camera app. Tap the gear icon at the top left (or bottom left if you're holding the phone landscape). Scroll down that menu all the way to the bottom. The second to last option says "Storage." Tap that and select "Memory card." Pictures will now be saved in a folder called "DCIM" on your SD card. If you're using a third-party camera app, there should be a similar option in the settings.
