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public void repaint() {
            // screen is a JFrame Object
    screen.repaint();
}

Main class

package game;

public class Main {

public static void main(String[] args) {
    Game game = new Game("Mein erstes Spiel", 800, 600);
    
    long lastFrame = System.nanoTime();
    
    while(game.isRunning()) {
        long thisFrame = System.nanoTime();
        float timeSinceLastFrame = ((float)(thisFrame-lastFrame))/100000f;
        lastFrame=thisFrame;
        
        game.nextState();
        game.update(timeSinceLastFrame);
        game.repaint();
    }

}

}

public void repaint() {
            // screen is a JFrame Object
    screen.repaint();
}

Main class

package game;

public class Main {

    public static void main(String[] args) {
        Game game = new Game("Mein erstes Spiel", 800, 600);
        
        long lastFrame = System.nanoTime();
        
        while(game.isRunning()) {
            long thisFrame = System.nanoTime();
            float timeSinceLastFrame = ((float)(thisFrame-lastFrame))/100000f;
            lastFrame=thisFrame;
            
            game.nextState();
            game.update(timeSinceLastFrame);
            game.repaint();
        }

    } 

}

Update 2:

I updated my code to:

        // Move the player
        x = playerRec.x += (int) (dx * timeSinceLastFrame * 500);
        y = playerRec.y += (int) (dy * timeSinceLastFrame * 500);

My player is moving, but not at the same speed and not very smooth: http://screencast.com/t/pv5M9Un4QhFR

public void repaint() {
    screen.repaint();
}

public void repaint() {
            // screen is a JFrame Object
    screen.repaint();
}

public void update(float timeSinceLastFrame){
    if (Mouse.isMouse(MouseEvent.BUTTON3)) {
        targetX = Mouse.getX();
        targetY = Mouse.getY();
    }

    if ((targetX != 0 && targetX != x) && (targetY != 0 && targetY != y)) {
        float dx = (float) (targetX-x);
        float dy = (float) (targetY-y);
        
        // normalize
        float length = (float) Math.sqrt(dx*dx+dy*dy);
        dx/=length;
        dy/=length;
        
        // add speed
        x = dx * timeSinceLastFrame * 300;
        y = dy * timeSinceLastFrame * 300;
        
        // Move the player
        playerRec.x = (int) x;
        playerRec.y = (int) y;
    }

}

package game;

import java.awt.Color;
import java.awt.Graphics;
import java.awt.Rectangle;
import java.awt.event.MouseEvent;

import javax.swing.JLabel;

public class Player {
    private Rectangle playerRec;
    float x, y;
    PlayerJLabel playerJLabel;
    int worldX = 800;
    int worldY = 600;
    int targetX, targetY;
    
    
    public Player(int posX, int posY, int size){
        playerRec = new Rectangle(posX, posY, size, size);
        x = posX;
        y = posY;
        
        playerJLabel = new PlayerJLabel();
        playerJLabel.setBounds(0, 0, 800, 600);
        
        Game.screen.add(playerJLabel);
    }

    
    public void update(float timeSinceLastFrame){
        
        if (Mouse.isMouse(MouseEvent.BUTTON3)) {
            targetX = Mouse.getX();
            targetY = Mouse.getY();
        }

        if ((targetX != 0 && targetX != x) && (targetY != 0 && targetY != y)) {
            float dx = (float) (targetX-x);
            float dy = (float) (targetY-y);
            
            // normalize
            float length = (float) Math.sqrt(dx*dx+dy*dy);
            dx/=length;
            dy/=length;
            
            // add speed
            x = dx * timeSinceLastFrame * 300;
            y = dy * timeSinceLastFrame * 300;
            
            // Move the player
            playerRec.x = (int) x;
            playerRec.y = (int) y;          
            
        }

    }
    
    
    private Rectangle getRec(){
        return playerRec;
    }
    
    
    public class PlayerJLabel extends JLabel{
        @Override
        protected void paintComponent(Graphics g) {
            super.paintComponent(g);
            g.setColor(Color.RED);
            g.fillRect(getRec().x, getRec().y, getRec().width, getRec().height);
        }
    }

}

Edit: I have a GameState method which calls the player update() method and a repaint() method which repains the whole scene.

GameState update method:

@Override
public void update(float lastFrame) {
    player.update(lastFrame);
}

Game repaint method:

public void repaint() {
    screen.repaint();
}

Main class

package game;

public class Main {

public static void main(String[] args) {
    Game game = new Game("Mein erstes Spiel", 800, 600);
    
    long lastFrame = System.nanoTime();
    
    while(game.isRunning()) {
        long thisFrame = System.nanoTime();
        float timeSinceLastFrame = ((float)(thisFrame-lastFrame))/100000f;
        lastFrame=thisFrame;
        
        game.nextState();
        game.update(timeSinceLastFrame);
        game.repaint();
    }

}

}