Ring sizing is very important. I highly recommend stopping by a local jewelry shop or department store and ask them to be sized. They should be happy to do it, and it should be free. Make sure to try on the correct type of ring sizers. If you are planning on purchasing a wide ring, then get sized for a wide ring. They feel tighter than skinny rings and often need to be sized abut a half a size larger.
You can also purchase a set of inexpensive plastic ring sizers like the ones pictured. I keep these stocked in my office so if you are not in a hurry, let me know and I can arrange to send you a pair if you are unable to make it to a jewelry or department store for sizing.
Each size is marked as either a full size, or a half size. These plastic ring sizers are accurate, inexpensive and can be used as many times as you need for sizing.
There are many other methods for determining your ring size, but these are the only two ways that I have found to be reliable.
Paper strips, zip-tie style sizers, printable gauges, string and calipers are all sure fire ways to get the wrong size, and end up ordering something that does not fit.
On a hot day, your fingers may swell up to a full size. When it is cold, I have noticed that my fingers are about a quarter size smaller that they are normally. Other factors can also contribute to a size fluctuation. Keep this in mind.
Not from the US? Not a problem. I use this handy chart to convert ring sizes: http://en.wikipedia.org/wiki/Ring_size
Lastly, Here is a video I shot on do it yourself ring sizing, which demonstrates the importance of proper sizing.
Here is an updated video with extra wide sizers: