With New 3DS XL hitting stores this week, Nintendo has posted an informative video showing you how to copy save data over to the new handheld.
The tutorial video shows you how to transfer data off the system as well as off the SD card.
Apparently, as Destructoid notes, you will need to use a #0 Philips screwdriver (the very tiny ones) and a microSD card.
The video explains it better, but her's a rundown: select system transfer in the system settings for each 3DS; copy SD data to a PC, then from there onto your microSD.
You can use wireless transfer if you prefer.
Nintendo has also posted extra details over on its support site.