How to install MySQL JDBC drivers into the standard Java path
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download/get the MySQL jdbc package file (i.e. mysql-connector-java-5.0.4.zip)

verify content of the file: jar -tf mysql-connector-java-5.0.4.zip
fm@DDM1307811:~> /usr/java/jdk1.5.0_09/bin/jar -tf mysql-connector-java-5.0.4.zip
mysql-connector-java-5.0.4/
mysql-connector-java-5.0.4/debug/
mysql-connector-java-5.0.4/docs/
mysql-connector-java-5.0.4/docs/release-test-output/

Either add the directory containing mysql-connector-java-5.0.4.zip to the classpath
or:
copy the extracted mysql-connector-java-5.0.4.jar to $JAVA_HOME/jre/lib/ext (i.e. /usr/java1.2/jre/lib/ext)
DDM1307811:/home/fm # cp mysql-connector-java-5.0.4-bin.jar /usr/java/jdk1.5.0_09/jre/lib/ext/
DDM1307811:~ # ls -l /usr/java/jdk1.5.0_09/jre/lib/ext/
total 9984
drwxr-xr-x   2 root root    4096 Dec 18 08:52 .
drwxr-xr-x  16 root root    4096 Oct 23 12:58 ..
-rw-r--r--   1 root root    8176 Oct 12 20:45 dnsns.jar
-rw-r--r--   1 root root  802388 Oct 23 12:58 localedata.jar
-rw-r--r--   1 root root  495944 Oct 20 00:17 mysql-connector-java-5.0.4-bin.jar
-r--r--r--   1 root root  158417 Oct 12 20:26 sunjce_provider.jar
-r--r--r--   1 root root  175811 Oct 12 20:26 sunpkcs11.jar

verify jdbc connection to database:

vi JdbcTest.java

//JdbcTest.java
import java.sql.Connection ;
import java.sql.DriverManager ;
import java.sql.ResultSet ;
import java.sql.Statement ;
import java.sql.SQLException;

class JdbcTest
{
  public static void main (String args[])
    {
      try {
        Class.forName("com.mysql.jdbc.Driver");
       }
        catch (ClassNotFoundException e) {
            System.err.println (e) ;
            System.exit (-1) ;
        }
       try {

            // open connection to database
           Connection connection = DriverManager.getConnection(
             // "jdbc:mysql://destinationhost/dbname?user=dbuser&password=dbpassword"
	     // MySQL internal data catalog is in a database called "mysql"
             "jdbc:mysql://localhost/mysql?user=root&password=test"
            );
            // build query, here we use table "User" in db "mysql"
            String query = "SELECT * From User" ;

            // execute query
            Statement statement = connection.createStatement () ;
            ResultSet rs = statement.executeQuery (query) ;

            System.out.println ("Query:") ;
            while ( rs.next () )
                // display content from column "User"
                System.out.println (rs.getString ("User")) ;
            connection.close () ;

        }
        catch (java.sql.SQLException e) {
            System.err.println (e) ;
            System.exit (-1) ;

        }
    }
}

Make sure there is a db user and this user got the correct access rights, i.e. to connect from remote systems.

Literature:

http://dev.mysql.com/doc/refman/5.0/en/connector-j.html