You’ll need Site Collection Administration access …
Site Actions > Site Settings > Audit log reports > Content Activity Reports > Deletion ….
Save this as an .xlsx, then within the workbook go to worksheet “Report Data 1” — . If your system has user IDs, then you can search the directory for their name.
Neel's Sharepoint Blog 
What if the site collection auditing was never turned on? Is there perhaps a way to look in the WFE logs directory to find something like this?
Hi I just found this blog while researching an issue we are having. We have a discussion board set up with various users – some are linked via Outlook, some are not.
Randomly when users are not logged into either their email and/or Sharepoint 2010 – I will get notices that mulitple posts are being deleted from the discussion.
We use the discussion board to track our CAB discussions for major changes in our environment so currently they are the only users (2nd level directors). Is there some setting that we can change that will stop the random deletion? Our Admin is also researching this but is coming up empty. Would changing the individual user’s permissions stop this action?
I believe they all have contributor permission – is there a way to all them to post, but not delete/edit the posts?
Thanks for any assistance you may provide.
Michelle
Michelle,
Sorry for replying late, hope you might have resolved it by now
Best way I know of is to create a new Security group with add-edit permissions pnly, so users in this group can only add/edit the information.
Let me know
Thank you
Neel
Very informative steps, I found an automated tool named LepideAuditor for SharePoint ( http://www.lepide.com/sharepoint-audit/ ) that helps to know who deleted files in SharePoint environment and show the data in the audit logs for a site collection