You can get this by following the steps outlined here

Summary:

1. The web app is not already installed
2. Meets a user engagement heuristic
3. Be served over HTTPS
4. Includes a web app manifest that includes:
   • short_name or name
   • icons - must include a 192px and a 512px icon
   • start_url
   • display - must be one of fullscreen, standalone, or minimal-ui
   • prefer_related_applications must not be present or be false
5. Registers a service worker with a fetch handler(read about service workers here)

As you can see, the interesting file to include on your website is a web app manifest JSON file.

Below is an example of a manifest file and how you can include it in your website HTML file.

{
  "short_name": "Weather",
  "name": "Weather: Do I need an umbrella?",
  "icons": [
    {
      "src": "/images/icons-vector.svg",
      "type": "image/svg+xml",
      "sizes": "512x512"
    },
    {
      "src": "/images/icons-192.png",
      "type": "image/png",
      "sizes": "192x192"
    },
    {
      "src": "/images/icons-512.png",
      "type": "image/png",
      "sizes": "512x512"
    }
  ],
  "start_url": "/?source=pwa",
  "background_color": "#3367D6",
  "display": "standalone",
  "scope": "/",
  "theme_color": "#3367D6",
  "shortcuts": [
    {
      "name": "How's weather today?",
      "short_name": "Today",
      "description": "View weather information for today",
      "url": "/today?source=pwa",
      "icons": [{ "src": "/images/today.png", "sizes": "192x192" }]
    },
    {
      "name": "How's weather tomorrow?",
      "short_name": "Tomorrow",
      "description": "View weather information for tomorrow",
      "url": "/tomorrow?source=pwa",
      "icons": [{ "src": "/images/tomorrow.png", "sizes": "192x192" }]
    }
  ],
  "description": "Weather forecast information",
  "screenshots": [
    {
      "src": "/images/screenshot1.png",
      "type": "image/png",
      "sizes": "540x720"
    },
    {
      "src": "/images/screenshot2.jpg",
      "type": "image/jpg",
      "sizes": "540x720"
    }
  ]
}

To include it in your web application add this tag in the head of all your pages of the website. Read more here.

<link rel="manifest" href="/manifest.json">

I hope this was helpful.