Once you install oracle in Linux system, connect with PuTTY or on Linux console and try to connect with oracle with sqlplus, although there are various ways to connect it from others tools provided by third party organization and through oracle as well, so there are various ways to connect with oracle through sqlplus, let discuss them one by one.
·         One way to connect it simply type sqlplus on Linux console, it ask for username and password and if your provided credentials are correct, then you will connect to oracle.
sqlplus_connect_1

·         Second way to connect it provide username with sqlplus, so it will only ask for password and if password provided is correct, then you will connect to oracle

sqlplus_connect_2
·         Third way to connect it provide full credentials with sqlplus, but in this case if anyone doing shoulder suffering can see your password and this can be security violation, so it is not recommended.
sqlplus_connect_3
·         Fourth way to connect sqlplus with easy connect, this is quite same as above one, But here we also mentioning ORACLE_SID with credentials, like in some case we have many oracle version, oracle database running on same Server, in that case we have to connect with specific ORACLE_SID. Let me show with screenshot. One more thing when you try to connect it with ORACLE_SID, you oracle listener should be in running condition, otherwise you will get an error (ORA-12541: TNS:no listener). So start Listener
[oracle@srv200 ~]$ sqlplus hr/hr@srv200
SQL*Plus: Release 11.2.0.1.0 Production on Fri Jun 28 15:17:01 2013
Copyright (c) 1982, 2009, Oracle.  All rights reserved.
ERROR:
ORA-12541: TNS:no listener   #error comes when listener is not running
Enter user-name:
[oracle@srv200 ~]$ lsnrctl start  # Start your listener
LSNRCTL for Linux: Version 11.2.0.1.0 – Production on 28-JUN-2013 15:17:15
Copyright (c) 1991, 2009, Oracle.  All rights reserved.
Starting /opt/app/oracle/product/11.2.0/db_1/bin/tnslsnr: please wait…
TNSLSNR for Linux: Version 11.2.0.1.0 – Production
System parameter file is /opt/app/oracle/product/11.2.0/db_1/network/admin/listener.ora
Log messages written to /opt/app/oracle/diag/tnslsnr/srv200/listener/alert/log.xml
Listening on: (DESCRIPTION=(ADDRESS=(PROTOCOL=ipc)(KEY=EXTPROC1521)))
Listening on: (DESCRIPTION=(ADDRESS=(PROTOCOL=tcp)(HOST=srv200)(PORT=1521)))
Connecting to (DESCRIPTION=(ADDRESS=(PROTOCOL=IPC)(KEY=EXTPROC1521)))
STATUS of the LISTENER
————————
Alias                     LISTENER
Version                   TNSLSNR for Linux: Version 11.2.0.1.0 – Production
Start Date                28-JUN-2013 15:17:15
Uptime                    0 days 0 hr. 0 min. 0 sec
Trace Level               off
Security                  ON: Local OS Authentication
SNMP                      OFF
Listener Parameter File   /opt/app/oracle/product/11.2.0/db_1/network/admin/listener.ora
Listener Log File         /opt/app/oracle/diag/tnslsnr/srv200/listener/alert/log.xml
Listening Endpoints Summary…
  (DESCRIPTION=(ADDRESS=(PROTOCOL=ipc)(KEY=EXTPROC1521)))
  (DESCRIPTION=(ADDRESS=(PROTOCOL=tcp)(HOST=srv200)(PORT=1521)))
The listener supports no services
The command completed successfully
After successful start of listener you can try connect it again
[oracle@srv200 ~]$ sqlplus hr/hr@srv200
SQL*Plus: Release 11.2.0.1.0 Production on Fri Jun 28 16:17:52 2013
Copyright (c) 1982, 2009, Oracle.  All rights reserved.
Connected to:
Oracle Database 11g Enterprise Edition Release 11.2.0.1.0 – Production
With the Partitioning, OLAP, Data Mining and Real Application Testing options
SQL>
·         Fifth way to connect oracle through sqlplus for sys user, this is for those user which were already authenticate by OS itself. For this any user that comes under the dba group can connect oracle without providing any credentials as sys as sysdba.
sqlplus_connect_4
·         Sixth way to connect oracle without any login, credentials, privileges. In this you can further connect with any other user.
sqlplus_connect_5