Classpath

Determine the classpath in effect at runtime by querying a System property.

String classpath = System.getProperty( "java.class.path" );

Excerpt of classpath that contains MySQL JDBC driver, while running within my IDE (IntelliJ).

…/com/mysql/mysql-connector-j/9.0.0/mysql-connector-j-9.0.0.jar:…

Dependencies

Manually downloading, installing, and configuring libraries needed by your project, such as JDBC drivers, is an annoying and troublesome chore. Automate it.

Java work is so much easier with a build management tool like Apache Maven or Gradle. Either of these tools is well worth the time taken to learn their basics.

Either of those tools will locate a copy of any needed libraries that you specify, download them from a repository on the internet, and install them appropriately into your project.

If using Maven, create a new project using a Maven archetype like Quickstart. The new project includes a POM file for you to edit.

Specify the JDBC driver as a dependency.

  <!-- https://mvnrepository.com/artifact/com.mysql/mysql-connector-j -->
  <dependency>
    <groupId>com.mysql</groupId>
    <artifactId>mysql-connector-j</artifactId>
    <version>9.0.0</version>
    <scope>compile</scope>
  </dependency>

Notice the scope element with value compile. That tells Maven to obtain a copy of the JDBC driver, use that copy for compiling, and include a copy into the final software artifact (likely a JAR file). See manual.

In a Web app, rather than a desktop app (console or GUI), you may want instead a scope of provided if you expect the JDBC driver to be already installed on your Jakarta Servlet container/server.

Code

Looks like your JDBC code came from an outdated tutorial. Here are some improvements.

Class.forName("com.mysql.cj.jdbc.Driver");

Calling Class.forName has been unnecessary for many years now. JDBC was rearchitected long ago to automatically load and register all available JDBC drivers via Java Service provider interface (SPI).

Make a habit of using DataSource interface & implementation. In real work, this enables you to eventually externalize your database connection info (username, password, server address, etc.) outside of your source code. In the meantime, write a method like this:

private DataSource dataSource ( )
{
    com.mysql.cj.jdbc.MysqlDataSource dataSource = new com.mysql.cj.jdbc.MysqlDataSource();  // Implementation of `DataSource`.
    dataSource.setServerName( "localhost" );
    dataSource.setPortNumber( 3306 );
    dataSource.setDatabaseName( "example_db_" );
    dataSource.setUser( "scott" );
    dataSource.setPassword( "tiger" );
    return dataSource;
}

Use try-with-resources syntax to simplify your code while automatically closing your opened database resources.

String sql = … ;
try
(
    Connection connection = dataSource.getConnection() ;
    Statement statement = … ;
    ResultSet resultSet = … ;
)
{
    … Handle your ResultSet. 
}
catch ( … )
{
    … Handle error conditions.
}
// Your Connection, Statement, and ResultSet objects will all be closed at this point, even if Exception is thrown.

You will find the source code for multiple full example apps demonstrating JDBC with MySQL, H2, and Postgres written by me, not to mention other great existing material on Stack Overflow. Search to learn more.

Example POM

Here is an example of a Maven POM created by Quickstart archetype, then adjusted by me to update all versions, and to use Aggregator edition of JUnit Jupiter.

<?xml version="1.0" encoding="UTF-8"?>

<project xmlns="http://maven.apache.org/POM/4.0.0"
         xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance"
         xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd">
    <modelVersion>4.0.0</modelVersion>

    <groupId>work.basil.example</groupId>
    <artifactId>ExMySql</artifactId>
    <version>1.0-SNAPSHOT</version>

    <name>ExMySql</name>
    <!-- FIXME change it to the project's website -->
    <url>http://www.example.com</url>

    <properties>
        <project.build.sourceEncoding>UTF-8</project.build.sourceEncoding>
        <maven.compiler.release>22/maven.compiler.release>7</maven.compiler.release>
    </properties>

    <dependencies>

        <!-- https://mvnrepository.com/artifact/org.junit.jupiter/junit-jupiter -->
        <dependency>
            <groupId>org.junit.jupiter</groupId>
            <artifactId>junit-jupiter</artifactId>
            <version>5.11.0</version>
            <scope>test</scope>
        </dependency>

        <!-- https://mvnrepository.com/artifact/com.mysql/mysql-connector-j -->
        <dependency>
            <groupId>com.mysql</groupId>
            <artifactId>mysql-connector-j</artifactId>
            <version>9.0.0</version>
            <scope>compile</scope>
        </dependency>

    </dependencies>

    <build>
        <pluginManagement><!-- lock down plugins versions to avoid using Maven defaults (may be moved to parent pom) -->
            <plugins>
                <!-- clean lifecycle, see https://maven.apache.org/ref/current/maven-core/lifecycles.html#clean_Lifecycle -->
                <plugin>
                    <artifactId>maven-clean-plugin</artifactId>
                    <version>3.4.0</version>
                </plugin>
                <!-- default lifecycle, jar packaging: see https://maven.apache.org/ref/current/maven-core/default-bindings.html#Plugin_bindings_for_jar_packaging -->
                <plugin>
                    <artifactId>maven-resources-plugin</artifactId>
                    <version>3.3.1</version>
                </plugin>
                <plugin>
                    <artifactId>maven-compiler-plugin</artifactId>
                    <version>3.13.0</version>
                </plugin>
                <plugin>
                    <artifactId>maven-surefire-plugin</artifactId>
                    <version>3.3.0</version>
                </plugin>
                <plugin>
                    <artifactId>maven-jar-plugin</artifactId>
                    <version>3.4.2</version>
                </plugin>
                <plugin>
                    <artifactId>maven-install-plugin</artifactId>
                    <version>3.1.2</version>
                </plugin>
                <plugin>
                    <artifactId>maven-deploy-plugin</artifactId>
                    <version>3.1.2</version>
                </plugin>
                <!-- site lifecycle, see https://maven.apache.org/ref/current/maven-core/lifecycles.html#site_Lifecycle -->
                <plugin>
                    <artifactId>maven-site-plugin</artifactId>
                    <version>3.12.1</version>
                </plugin>
                <plugin>
                    <artifactId>maven-project-info-reports-plugin</artifactId>
                    <version>3.6.2</version>
                </plugin>
            </plugins>
        </pluginManagement>
    </build>
</project>