Linux command to find and delete certain files, but output the result or verbose mode?

find also has a -delete flag. And you could also combine everything into one command, possibly saving some time:

find . \( -name .DS_Store -or -name ._.DS_Store -or -name Thumbs.db -or -name ._Thumbs.db \) -print -delete

Just add the -v parameter to the rm command for verbose output, e.g.

find . -name .DS_Store -printf \"%p\"\ \  | xargs rm -v