A very easy way to connect to a specific SID (other than the default one) using sqlplus, is to make this SID “temporarily” the default SID.
Just change ORACLE_SID environment variable to the required SID name:
export ORACLE_SID=sid_name
Then connect using sqlplus to the default SID:
sqlplus / as sysdba
It may not be the ideal way, but it’s “simple and stupid” as  SoCRaT says 🙂