Find and delete files 1 week old (or older)

find /data/files -type f -name "*.txt" -mtime +7 -exec rm {} \;

/data/files - directory
-type f  - find files, not directories, etc
-name "*.txt" - specify file type if necessary
-mtime +7 - modified 7 days or more.  Last accessed time is -atime
-exec rm {}\; - execute rm with the results returned from 'find'

OR

find /data/files -type f -name "*.txt" -mtime +7 | xargs rm