Here is the safest (and hopefully quickest) way to get stuff transfered without losing any data:

• Go to the SD Card Association's website and download the latest SD Card Formatter from their website (lowest left button for Windows, lowest right for Mac).

• Install the program on your computer. After doing so, insert your brand new SD card into the SD Card slot and run the SD Card Formatter.

• On the topmost left hand side is the "Drive" selection (the one that says "B:","D:","E:","F:", etc. whatever alphabet). Select the appropriate drive that corresponds to your SD Card slot (If you SD card slot is Drive "S:" then choose "S:" by clicking on the drop down menu).
• On the bottom right (on top of the "Exit" button) is the Options. Click it, and on the "Format type" option, click the drop down menu and choose "Full (Overwrite)". Leave the "Format Size Adjustment" setting to "Off".
• Click OK to exit the Option Settings menu. (If you want to name your SD card, you may choose to put one on the box beside "Volume Label:", but make sure not to leave any spaces. Otherwise just leave it blank.)
• Click Format. Wait for the SD Card Formatter to complete formatting. It usually takes a couple of minutes. Usually more the bigger the capacity...
• After the confirmation screen pops up, click OK. And select Exit from the SD Card Formatter program on the bottom right.
• Now create a new folder on your Desktop. Name it "3DS" or whatever is easiest to remember.

Now onto the SD Card on the 3DS:

• Make sure to Power Off your 3DS before taking out the SD Card. Do not leave it in Suspend Mode. It must be powered off completely.
• Saftely eject you brand new SD Card from your computer and insert the SD Card you were using for your Nintendo 3DS. Then open the root directory of your SD Card drive.
• Now select all the items in the SD card and Copy them to your new folder in the Desktop. Once again this takes a while.
• Now saftely eject your old 3DS SD Card from your computer and insert the new SD Card you just formatted in. Keep the old SD Card for backup.
• Open your new folder in the Desktop and again copy the entire contents from it. Do not copy the new folder itself! You need the directories Nintendo 3DS and DCIM, and whatever else is in there to be copied onto the root directory of the brand new SD card. Paste the contents to the new SD Card. Again this takes time so wait for it to finish completely.
• Saftely eject the new SD Card and insert it into your 3DS. Power your 3DS back on and see if your menu boots up correctly. Try some 3DSWare software to see if everything is functioning properly.

Basically the gist of formatting the card is:

• Making sure the new SD Card you are about to use complies with the standards set by the SD Association, of which Nintendo is an Execitve Member of (in other words, your SD Card is not formatted in some other way Nintendo devices won't recognize).
• Making sure you transfer the files to the root directory of the SD Card and not inside a folder. Both the Wii and 3DS folders and files should remain in the same directories they were prior to transfering.

While the former is not really required with regards to data transfer, it obviously helps in case you do run into problems like errors, or you just came from buying a brand spankin' new SD Card only to find it "wont work".