First, I would recommend to install some third party softwares to analize the logs files for you every early morning and send an email.
For example:
http://www.logwatch.org/
http://sourceforge.net/projects/psad/
Read their documentation and install it at your own risk.
There are several good ones but do a search on google and you'll find out more.
Do a cat /etc/syslogd.conf, all your logs will be recorded according to the configuration inside the file syslogd.conf
Read them carefully and do a search on google when it's neccesery.
Configure iptables or ipchains to access only the ports that are considered being used. Or maybe install a firewall to do that for you.
No machines are completely secured and every of them brings the chance of being compromised. Make sure all your packages are up-to-date. If you think it's neccesery, either you have to do lots of reading or hire a sys admin dedicate to taking care your server.