Now first off, this is not in any way the best dock option for a New 3DS XL. It's not the most pretty looking, it's simply just a cheap and easy way to have a dock that works with no extra purchases . If you want a nice dock, then go buy the new one that is meant to be used with the New 3DS XL.
Otherwise, this is a very easy modification and all you need is some glue, a pocket saw, and some sandpaper.
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Step 1: Remove the Edges in the Way.
Use a small saw or pocket saw (or a Dremel tool if you want) to remove the bottom edge and top left bit. (Circled) Save the bottom pieces.
Step 2: Sand the Edge
Use a course sandpaper to flatten the bottom edge.
Step 3: Glue the Pieces to the Back
Glue the pieces kept from earlier to the back of the dock as to hold the 3DS XL system in place. You will need to place the new 3DS on the dock first to find where to glue the pieces to hold it against the charger.
Step 4: Enjoy Your Modded Dock
Like I said, not the most pretty looking, but it works. :)