Doctors Without Borders typically want experienced nurses with Critical Care or OR experience - it's a competitive organization with significant commitment of usually a year. They usually only give shorter assignments to those they really need, like surgeons.
Try volunteering in your home city! You'll be most effective in a setting where you belong and are accepted by the community, and you'll use resources more efficiently. Get in touch with your county health department - they usually coordinate with a number of volunteer organizations in everything from STD education and testing, to teaching safety classes to seniors. I know my county also has an emergency volunteer registry, where you'll be contacted in event of a crisis (I was on standby for the G20 summit this past summer).
While the adventure of overseas volunteering is attractive, you need to build up some awesome skills before it's worth anyone's time. But don't be discouraged, definitely volunteer!