Some states provide this information online and you can find inmates through a quick search. Others offer a name search option for you to find the chosen inmate. For places that do not have a list online you can usually ring the sheriff's office and they will furnish you with the necessary information over the phone.
You will be given the inmates registered inmate number and you should be able to contact him through that.
There are plenty of inmate searches that are available from the Department of Corrections available as well as a state-wide sex offender's register for those that have committed sex offences in the State of Washington.
If you know the name of the person you can send them mail to the jail address. Just put their name on top of the letter and the address of the jail below. They should receive it if they are there and you should just ask them to contact you through the letter. If they return a call or a letter you know they are in that jail.
The address is
c/o Mason County Jail
P.O. Box 519
Shelton, WA 98584
These are the easiest ways to find a person who is in jail in the Washington State area and for you to get in contact with the individuals in question.