Source: Finder doesn’t work since Yosemite – Ask Different [WayBack]:
This fix from Reddit worked perfectly for me!!
http://www.reddit.com/r/osx/comments/2jtikj/finder_not_responding_new_yosemite_install/ [WayBack]
You can most likely fix the issue by clearing out Finder’s saved state, caches, and/or settings.
Use Spotlight (the search icon in the far right of the menu bar) to find and open the “Terminal” application. Triple-click the following line in order to copy and paste it into Terminal’s window:
rm -fR ~/Library/Saved\ Application\ State/com.apple.finder.savedState ~/Library/Caches/com.apple.finder; killall Finder
If it still doesn’t work, try this one:
mv ~/Library/Preferences/com.apple.finder{,.backup}.plist; killall Finder
–jeroen