The number of days depends on what you mean by "once the process is started", how soon the landlord schedules the hearing, and how soon the sheriff wants to come by to remove the tenant. The answer assumes a residential landlord-tenant case.
If "once the process is started" is counted from the date the complaint is filed with the court and served on the tenant, RCW 59.18.370 (Forcible entry or detainer or unlawful detainer actions — Writ of restitution — Application — Order — Hearing) provides that the hearing "shall not be less than seven nor more than thirty days from the date of service of the order upon defendant." The statutes are at http://apps.leg.wa.gov/rcw/default.aspx?cite=59.18 .
RCW 59.18.410 (Forcible entry or detainer or unlawful detainer actions — Writ of restitution — Judgment — Execution) provides when the sheriff can first come by to remove the tenant. In some cases, as specified in the statute, the tenant still has an opportunity to stop the sheriff by paying the judgment.
Many sheriff departments need more days than allowed by RCW 59.18.410 for a deputy to have time to come out to the rental property to supervise the removal of the tenant and the tenant's properties. Because the sheriff wants to take the tenant by surprise, the sheriff would not disclose to the tenant the exact date and time will be showing up at the property. The writ would disclose only a time and date after which the sheriff can show up.
If you have no money to pay for rent and no defense as to why you should not be removed, you likely should plan of being removed from the property in as little as 3 weeks.
There are volunteer attorneys and organizations that provide help to tenants facing eviction. The groups providing volunteer service to tenants often have offices in the courthouse.
You should review your specific facts with your attorney to find out your legal options.