What audit methods do I have in Linux server? If I want to audit specific user commands? That commands he used and at what time?

last username will show you the login session of the particular user in the machine

vi /home/username/.bash_history will show you the commands which was executed by the particular user.

You can use history command. 

For time stamp export HISTTIMEFORMAT variable.

TO know more on this

To audit specific user command ./bash_history may be useful.

To know more please visit: 

http://www.tecmint.com/history-command-examples/