I assume you want to design scemas for tables within a database that is supported by a pre-developed RDMBS package.
If that is a good assumption, then download MySql.
MySQL :: The world's most popular open source database Its open source, free, robust, well supported, etc.
Use JDBC to connect your Java code to the MySql database engine, after you have created your database, created your tables, etc.
If you want to write your own RDBMS package, that is a great thing, it was a standard one semester assignment when I was in grad school. But its fairly hard, it takes a full semister to do.