I guess you are using ‘Express Edition’.
Please provide a little more information.
Are you trying to connect from a remote client, or locally ?
Were you able to connect from SQL*Plus before, or you have never been able to connect ?
Have you made changes to some database parameter (such as SGA size) ?
What is the operating system (database server and client) ?
You might find some useful information in the oradim log, which is usually under <oracle_home>\app\oracle\product\10.2.0\server\database\ (on a windows server).
Is Oracle started : show SQL*Plus a IDLE-Message ?, if so, start the datebase:
Is the listener started ? use lsnrctl status, if not started, then use lsnrctl start