Why are the corners of my work curling?
It could be that you have too much tension on the corners. Make sure not to pull your stitches too tight when you are turning.

It's also possible this is just the natural pull of the material, and you aren't necessarily doing anything wrong. This is fairly common in knitting, but no reason it couldn't happen with crochet stitches too. The process of reshaping a finished article is called blocking. There are a few standard techniques you could try, depending on what type of yarn you used.

For natural fibers, the basic idea is:


Wet the piece
Stretch and shape to the desired size
Air dry (optionally while pinned to a blocking board; a cheap and common substitute is foam floor squares, like those used for play mats)


The process of wetting and drying will lock the fibers into place, similarly to felting. There are three main ways to do this:


Wet blocking is done by completely soaking the piece. Then, lay it on a towel and roll it up, squeezing out the excess water. After the water is wrung out, shape the article and let dry.
Steam blocking is done by placing a wet washcloth over the (dry) item, and ironing over top of it while gently shaping the article.
Spray blocking wets the article by spraying with room-temperature water, rather than soaking or steaming.


Whichever you choose, you will have to re-block the item after washing.

Acrylic yarn doesn't work with wet or spray blocking, since the fibers don't absorb water. Instead, you can use heat to melt the fibers enough to stay in place. There are two ways to do this:


Steam blocking with a low setting, and pressing with up and down motions rather than side-to-side
"Ironing" from a few inches away - never place the iron directly on the yarn, it will melt!


Always err on the side of caution! The extreme is to "kill" the yarn - melting it so much that it loses elasticity and cannot be frogged. Sometimes this is done on purpose, as the resulting material has a nice sheen and drape. If you want to do this, steam block with a higher setting until it achieves the desired properties.

Blocking acrylic with heat is permanent, and it will keep its shape after washing.