How do I delete a Google Doc but only for me and not other users that may have access to the document?

You cannot do this unless those people are also owners of the document. If you want to assign a document to another user as owner - just share it with them and set the permissions to OWNER.

After that - if you delete the file - it will only be removed for you. The other person will still have it.
See this site for more information.

http://support.google.com/drive/bin/answer.py?hl=en&answer=2494892&rd=1

Helpdesk