This is a list of what you need to transfer your content from your existing 3DS to the New 3DS XL System.
- The existing system
- The SD card
- New Nintendo 3DS XL system
- Micro SD card of equal or larger size
- A size 0 Phillips screwdriver
- A computer
- An adapter that will accept both sizes of SD cards
The above video from Nintendo explains the process, and needless to say it's going to be tricky to trade in your existing hardware and pick up a new one while still keeping your games, unless you find a story that's willing to let you complete the process on the premises. There will likely also be the option to transfer games strictly through the wireless connection, but expect a very long wait for your files to move over if you've downloaded many large games.
To install games you've already purchased on the PlayStation 4 or Vita, for reference, simply log into your account on the new hardware and begin the downloads.