Create a trigger, program unit or store function using SYS_CONTEXT function to get the IP address.

Example:
CREATE OR REPLACE Function IP
RETURN Varchar2
IS
v_ip Varchar2(30);
Begin
Select SYS_CONTEXT('USERENV','IP_ADDRESS')
Into v_ip
From Dual;
Return v_ip;
End;

For more information on the SYS_CONTECT function refer to:
Oracle8i Application Developer's Guide - Fundamentals.

You can do Select SYS_CONTEXT('USERENV','IP_ADDRESS') from dual;
in a SQL*Plus session if all you want is your IP address.