Purchase twill tape from a fabric or craft store. It is generally available in packs starting at 3 yards, but shorter lengths can often be cut at the fabric counter.
Cut the twill tape into four 12-inch segments.
Turn the duvet cover inside out over your work surface so that you have access to the interior side of the corners.
Sew a length of twill tape to each of the corners of the cover, making your stitches halfway along the length of twill tape (so that you have 6 inches of twill on each side of the seam).
Tie the bottom corners of the duvet to the bottom corners of the duvet cover using the newly attached twill tape (the cover should still be inside out at this point). A simple bow works best for tying the duvet to the cover, and is easy to untie when you need to remove and wash the cover in the future.
Turn the duvet cover right-side out again and shake the duvet into place from the bottom. The tied corners will hold the cover in place while you do so.
Tie the upper corners of the duvet to the upper corners of the cover with the twill tape, and shake once more to fluff everything into place.