How do I know if they've finished downloading?
You'll get a Spotpass message titled "Puzzle Swap," which indicates that the Spotpass puzzles are ready.
If you're still having trouble, refer to this step-by-step list I made awhile back:
- Format system.
- Connect to the internet and make sure the region is set to the US.
- Make a Mii.
- Start Streetpass Plaza.
- Set Spotpass settings in Streetpass Plaza to "On"
- Go to Puzzle Swap to get my first normal piece.
- Exit StreetPass Plaza.
- Close the 3DS and wait around 5 minutes for everything to download.
- Reopen Streetpass Plaza and tag the Special Mii.
- Go back to Puzzleswap and unlock the Spotpass puzzles by taking a free the free puzzle piece.
- Take whatever puzzle piece from the Special Mii.