If you are using Win OS, and using a Command prompt to start the sqlplus, you need to set environment parameter in the cmd prompt first.
1) set ORACLE_SID=<your SID>
2) sqlplus /nolog
after go into sqlplus,
3) connect / as sysdba
then you can connect the local SID. But if you connect to remote DB, you did not need to do this.
Markco Wong