WA is supposedly one of two states in which an applicant for a driver's license does not have to prove lawful permission to be in the US. If you have the required documents, you may be able to get a driver's license in WA even if you likely would have difficulty in obtaining one in most of the other states.
There is an ongoing investigation concerning persons without lawful immigration status coming to WA to obtain a commercial driver's license.
This webpage from the Department of Licensing has the information on what you need to get a driver's license in WA: http://www.dol.wa.gov/driverslicense/steps.html .
WA requires a driver to have at least a minimum level of liability insurance. If you are here only a short time, you should consider all the costs before getting the driver's license.