If the server in question is a Windows platform, go to Control Panel->Administrative Tools->Services. Look through the list for services that have a name of the form OracleServiceXXXX. The "XXXX" will be the database identifier or SID. There can be multiple services for multiple instances running on that machine.
If the server in question is a Unix or Linux platform, then you'll want to examine the oratab file. This file is commonly found in the /var/opt/oracle or /etc directories. In that file, there will be one line each instance on the server.
This was first published in September 2004