How to create a small and simple database using Oracle 11 g and SQL Developer

Question

How can I build a tiny, straightforward database with Oracle 11g and SQL Developer? I'm seeing entirely too many problems, and I can't figure out how to create a straightforward database. For instance:

create database company; 

Caused the following error:

Error starting at line 1 in command:
create database company
Error at Command Line:1 Column:0
Error report:
SQL Error: ORA-01501: CREATE DATABASE failed
ORA-01100: database already mounted
01501. 00000 -  "CREATE DATABASE failed"
*Cause:    An error occurred during create database
*Action:   See accompanying errors.