you should read the sendmail howto for info on how to get started.
www.tldp.org . check you have added the relevant relayable hosts in /etc/mail/access and are using a suitable relay method, e.g. access_db or relay_hosts_only which is defined in /etc/mail/sendmail.mc. generally tho these are pretty standard issues that should be tackled with the help of a manual or howto. if you hit a brick wall, come back.