Things You'll Need
Steamer or damp sponge/towel
heavy furniture or books
Never roll your rug the opposite way it came rolled up. This will break apart the glue and stitching holding the rug together.
Don't soak the rug if using the steam or wet towel method. Normally a damp towel works fine, something that will be dry in an hour or so.
If you have a smaller rug, and only one corner is sticking up, try placing a book on the end and an ice cube right on the corner. It seems silly, but it works.
Whenever you order or buy a new rug, assuming is has some size to it, you will get the rug in a roll. Normally these rugs have been rolled up for quite some time. When you get home and try to lay it down where you would like it, it will want to roll back up. Of course, over time the rug will eventually flatten out on its own, but that is assuming that you don't continually fold that edge over from stepping on it. Most people want it to lay flatter, faster.
Take either the steamer or the wet sponge/towel and dampen the edges of the unrolled rug. Allow this to dry this way and see if it helps. If it doesn't, continue on.
Lay a damp towel over the edges, and iron them flat. Many times, this will allow the rug to lay smooth for a while. If the ends still curl up, move to the next steps.
Lay the rug upside down. This will still take some time, but significantly less time that it would if it were right-side up. This method does work really well, but works best if you have an extra room or basement where you can do it. It isn't good for the rug to be walked on while it is upside down, nor does it look very attractive.
Lay the rug where you would like it to go, and then rearrange your furniture. Ensure that you place at least one piece of furniture on each corner of the rug. You won't have to leave your furniture this way forever, but 2 to 3 weeks should be sufficient.
Place heavy books, such as phone books, on the corners. This method doesn't work quite as well as the furniture method listed above, but it is an option if you don't have the space to move the furniture around.
Put the rug between the mattresses on your bed, on top of the box spring. This will normally flatten the rug in about a week, but only works if the rug is smaller than your mattress.