I use scene2d library for making UI elements in the screen like button,Text ,Image etc.

• Create a class start that extends the Game class and call setScreen function to set screen to main menu
• MainMenu Class implements screen.It have stage that contains buttons that also have on/off state ,An input listener is added to button to handle touch inputs

You can find button.pack and new.fnt files from here

Start Class

public class Start extends Game{
    public OrthographicCamera camera;
    public SpriteBatch batch;
    public BitmapFont font;
    

    
    @Override
    public void create() {
        
        camera=new OrthographicCamera(Constants.width,Constants.width*Constants.aspectRatio);
        batch=new SpriteBatch();
        
         
        setScreen(new MainMenu(this));
            
    }

}

MainMenu Class

public class MainMenu implements Screen{
        Start game;
         private Stage stage; //** stage holds the Button **//
            private BitmapFont font; 
            private TextureAtlas buttonsAtlas; //** image of buttons **//
            private Skin buttonSkin; //** images are used as skins of the button **//
            private TextButton button; 


public MainMenu(Start game)
{
    this.game=game;
    
}
    
        @Override
        public void show() {
        
        
        buttonsAtlas = new TextureAtlas("img/button/button.pack"); //**button atlas image **//
        buttonSkin = new Skin();
        buttonSkin.addRegions(buttonsAtlas); //** skins for on and off **//
        font = new BitmapFont(Gdx.files.internal("font/new.fnt"),false); //** font **//
       
        stage = new Stage();        //** window is stage **//
        stage.clear();
        Gdx.input.setInputProcessor(stage); //** stage is responsive **//
       
        TextButtonStyle style = new TextButtonStyle(); //** Button properties **//
        style.up = buttonSkin.getDrawable("buttonOff");
        style.down = buttonSkin.getDrawable("buttonOn");
        
        style.font = font;
       
        button = new TextButton("START", style); 
        //** Button text and style **//
        button.setHeight(Gdx.graphics.getHeight()/3); //** Button Height **//
        button.setWidth(Gdx.graphics.getWidth()/4); //** Button Width **//
       
        button.setPosition(Gdx.graphics.getWidth()/2-button.getWidth()/2, Gdx.graphics.getHeight());
        
        button.addListener(new InputListener() {
            public boolean touchDown (InputEvent event, float x, float y, int pointer, int button) {
                    Gdx.app.log("my app", "Pressed"); //** Usually used to start Game, etc. **//
                   
                 
                    // TODO Auto-generated method stub
                            
                
                
                    return true;
                    
            }
           
            public void touchUp (InputEvent event, float x, float y, int pointer, int button) {
                    Gdx.app.log("my app", "Rggggggeleased");
                 
              ///and level
                    game.setScreen(new MyNextScreen(game));
                    
                    dispose();
                    
            }
        });
       
       
        
        MoveToAction moveAction = new MoveToAction();//Add dynamic movement effects to button
        moveAction.setPosition(Gdx.graphics.getWidth()/2-button.getWidth()/2, Gdx.graphics.getHeight()/2+ Gdx.graphics.getHeight()/6);
        moveAction.setDuration(.5f);
        button.addAction(moveAction);
      
        stage.addActor(button);
        
    }
    @Override
    public void render(float delta) {
        // TODO Auto-generated method stub
         Gdx.gl.glClearColor(1, 1, 1, 1);
            Gdx.gl.glClear(GL20.GL_COLOR_BUFFER_BIT);
            stage.act();
         game.batch.begin();
            stage.draw();
           game.batch.end();
         
    }

    @Override
    public void resize(int width, int height) {
        // TODO Auto-generated method stub
        
    }

    @Override
    public void pause() {
        // TODO Auto-generated method stub
        
    }

    @Override
    public void resume() {
        // TODO Auto-generated method stub
        
    }

    @Override
    public void hide() {
        // TODO Auto-generated method stub
        
    }

    @Override
    public void dispose() {
        // TODO Auto-generated method stub
        
    }

}