Tack them into place with a sewing thread NOT embroidery thread as this thread is only temporary and will be removed later. Embroidery thread will leave behind a coloured mark.
Now if you are using a more Open Weave material you'll not want the stuffing to show through the holes so a piece of lining material should be used. It doesn't matter what as long as it's cotton and the colour of your aida. You could even use a bit of recycled material ie use DH old shirt
Also if you are concerned the folded corners might come free just use some correct colour cotton sewing thread to secure them making sure the stitches don't show through to the side where you design is.
Sew the cotton lining and again use a cotton sewing thread. Do not Worry too much about how neat your hand sewing is as long as it doesn't show through on the side of your design.. No one is ever going to see the inside. Once you have sewn the lining onto the back you can remove the 'tacking threads' (they were the temporary red sewing cotton line of sewing in the previous photo)
With your embroidery thread make sure its 2 strands thick attach to back of design and bring your needle up through the middle loop of any corner
Now fold your other piece in half to find the centre. (If unsure it's the centre count the number of holes along one side and divide by 2)
This is were you join the corner of your other square so bring the needle up through the centre loop.
Then whip stitch around your Biscourn so it looks like this (leaving a hole so you can stuff it)
Once stuffed, continue sewing up the last little opening.
It should resemble something like this
Now choose a couple of buttons with the same amount of holes in them ie 2 hole or 4 hole, don't bother with Shanked buttons it's just too hard.
With your sewing thread attach to the centre of the design on one side then pull your needle through the biscornu to the other side
Sew on the buttons taking your thread all the way through your biscornu pulling it tight. Back and forth through your button holes and the biscornu to the opposite button. Do this a few times then do a couple of slip knots around the base of one button remembering to pull tight. Then take your thread through the side of the Biscornu pull tight and snip. The end of the thread will disappear inside your Biscornu.