Here's an example of how to connect to an Apache Derby database in Java using JDBC:

1. Download and install Apache Derby

You can download Apache Derby from the official website: https://db.apache.org/derby/. Once you have downloaded the distribution, follow the installation instructions for your operating system.

2. Import the necessary packages

You need to import the necessary JDBC packages for connecting to a database. Here's an example:

import java.sql.Connection;
import java.sql.DriverManager;
import java.sql.SQLException;

3. Establish a connection to the database

You need to establish a connection to the database using the getConnection() method of the DriverManager class. Here's an example:

String url = "jdbc:derby://localhost:1527/mydatabase";
String username = "myuser";
String password = "mypassword";

try {
    Connection connection = DriverManager.getConnection(url, username, password);
} catch (SQLException e) {
    e.printStackTrace();
}

In this example, we are connecting to a Derby database with the URL "jdbc:derby://localhost:1527/mydatabase", and the username "myuser" and password "mypassword". Note that the URL includes the protocol jdbc:derby, the hostname and port localhost:1527, and the name of the database mydatabase.

4. Closing the connection

Once you are finished using the database, you should close the connection to free up resources. Here's an example:

try {
    connection.close();
} catch (SQLException e) {
    e.printStackTrace();
}

In this example, we are closing the connection object that was created earlier.

This is a basic example of how to connect to an Apache Derby database in Java using JDBC. There are many other options and configurations that can be used to fine-tune the connection, but this should get you started.