A simple script that loads a new scene async. and display the progress while loading.

StartMenu.cs

using System.Collections;
using System.Collections.Generic;
using UnityEngine;
using UnityEngine.UI;
using UnityEngine.SceneManagement;

public class StartMenu : MonoBehaviour
{
    [SerializeField]
    private string sceneName = "SampleScene";

    [SerializeField]
    private GameObject loadPanel = null;

    [SerializeField]
    private Text loadText = null;

    private void Start()
    {
        loadPanel.SetActive(false);
    }

    public void Play()
    {
        StartCoroutine(LoadSceneAsync());
    }

    private IEnumerator LoadSceneAsync()
    {
        AsyncOperation asyncLoad = SceneManager.LoadSceneAsync(sceneName);

        loadPanel.SetActive(true);

        while (!asyncLoad.isDone)
        {
            loadText.text = asyncLoad.progress + "%";
            yield return null;
        }
    }
}