The City of Seattle runs a program called Trees for Neighborhoods, which gives free trees and tree planting training to Seattle residents. Applications for this year’s cycle will open on July 31. You want to apply very, very quickly — this program fills up fast and there is a limited number of free trees available.
Please see this website: http://www.seattle.gov/trees/treesforneighborhoods.htm to apply. Here is the official document from the city (.pdf): Trees for Neighborhoods 2013