When we moved, Grandma J gave us two toddler beds and the double bed that Little Miss used to sleep in became the bed in the guest room once again. We found ourselves in need of more crib-sized fitted sheets, and with a surplus of girly double sheets. In case you were wondering, as you can see in the pictures below, a double sheet is almost exactly the size of two toddler bed sheets. So, naturally, Mommy got an idea.
See how, when folded in half, a double sheet hangs off a crib mattress? This is a perfect size, when the corners are fitted, for a crib mattress sheet. 
Also, notice the toddler in the picture. It is important to note the virtual impossibility of snapping a photo of a mattress on the floor in the presence of a toddler without said child bouncing on the bed. 
Another view, another child. Okay, here we go...
1. Fold your sheet in half. Cut along the fold line.
2. Finish the edge. Doesn't matter how. Serging it is fastest. I did that on one of the "new" sheets for sake of time and ease. On the other (in the pic), I folded the edge under and sewed a straight stitch to match the finished edge that was already on the sheet.
3. Looking at the corner of the sheet, you can easily see with a striped pattern that they meet at a 90 degree angle. This means that you can simply cut out a square and join the sides to make a new corner. This can be done by folding in one corner to make a triangle and cutting along the edges.
To find the size of the square I needed, I needed to know the length and location of the side of the corner that was already in the sheet. This was easy to find because of the stripes. I measured the seam of the existing corner to find the length, and followed the stripe across the sheet to find where the edge of my square needed to be placed on the long side of the sheet.
4. Place pins to mark where your edge should be. Fold in the corner to make a triangle, and pin in place to avoid fabric shifting as you cut. Cut two sides, using your triangle as a guide.
5. For the other corner, you can repeat step 4 or use the square that you just cut out as a guide. Just lay down the square that you just cut out, and cut around it.
6. Match your new raw edges, right sides of the sheet fabric facing. 
another pic of the edges matched up
7. Sew the raw edges together. Finish edge (zig-zag, serge, or fold over and hem).
8. To figure out how much elastic you need to fit your corner, simply measure the elasticized length of the sheet. Do NOT stretch it out for this part. (There are no red squiggly underlines showing up, so I'm assuming that "elasticized" is, indeed, a real word.) 
Obtain 2 lengths of elastic for this. Because I used re-purposed elastic--and, come to think of it, a gifted sheet--this was a completely free project for me!
9. Find the middle of the elastic. 
Mark it and match it up with the corner seam on the sheet. 
10. Holding onto the middle of the elastic (which is pinned to the sheet), pull the first half of your elastic as tight as it will go and find the point of the fabric it reaches to. Start sewing it from there. I think I used a multiple zig-zag stitch, set on the longest length and widest width. When you get to the middle of your elastic, take your pin out and keep sewing, pulling your elastic as tight as it'll stretch. 
11. And... you're done! If you're lucky your toddlers will be over the moon at the awesome sheets that Mommy just made. If you're really lucky, they'll give you a real boost by running to Daddy to gush about what a great job Mommy just did. This day, I was lucky. :)
