Trace and analyze logs on SQL Server
SQL Injection is hard to track from SQL Server side. If you want to find out who change what, then some sort of tracing should be running on your server.

If no tracing (custom one implemented by your company DBA or sysadmin) is running, then you can check 


windows event logs
sql server error logs
Default Trace for objects modified.
Successful and Failed logins (if you have enabled on sql server side).


Above all are few areas to look into, but it will be difficult for you to corelate and find a pattern.

Best is to scan your web-server IIS error logs using tools like LogParser.

Additional References :


SQL Injection: Defense in Depth
How to Secure Microsoft SQL Server