Enable general log http://dev.mysql.com/doc/refman/5.1/en/query-log.html
Also You can refer this blog post: http://serge.frezefond.com/2013/04/how-can-we-audit-a-mysql-server/
There are other ways as well for a detailed logging information for each and every query auditing:
Using MySQL audit plugins
There are audit plugins released by MySQL and some of the forks, you can try them if you are concerned about security on your MySQL server
1) MySQL Enterprise Audit
Enterprise Audit uses the open MySQL Audit API to enable standard, policy-based monitoring and logging of connection and query activity executed on specific MySQL servers.
2) McAfee Audit Plugin - Open source
designed with an emphasis on security and audit requirements. The plugin may be used as a standalone audit solution or configured to feed data to external monitoring tools.
3) MariaDB Audit plugin
Auditing regulations are used by many enterprises to ensure they comply with laws and industry standards. Such regulations often require processes for tracking user access to data in databases.
Refer my existing answer here MySQL query log