At the time of writing this answer, there was no method to embed which let the user navigate inside folders and view the files without her leaving the website (the method in other answers, makes everything open in a new tab on google drive website), so I made my own tool for it. To embed a drive, paste the iframe code below in your HTML:
<iframe src="https://googledriveembedder.collegefam.com/?key=YOUR_API_KEY&folderid=FOLDER_ID_WHIHCH_IS_PUBLICLY_VIEWABLE" style="border:none;" width="100%"></iframe>
In the above code, you need to have your own API key and the folder ID. You can set the height as per your wish.
To get the API key:
1.) Go to https://console.developers.google.com/ Create a new project.
2.) From the menu button, go to 'APIs and Services' --> 'Dashboard' --> Click on 'Enable APIs and Services'.
3.) Search for 'Google Drive API', enable it. Then go to "credentials' tab, and create credentials. Keep your API key unrestricted.
4.) Copy the newly generated API key.
To get the folder ID:
1.)Go to the google drive folder you want to embed (for example, drive.google.com/drive/u/0/folders/1v7cGug_e3lNT0YjhvtYrwKV7dGY-Nyh5u [this is not a real folder]) Ensure that the folder is publicly shared and visible to anyone.
2.) Copy the part after 'folders/', this is your folder ID.
Now put both the API key and folder id in the above code and embed.
Note: To hide the download button for files, add '&allowdl=no' at the end of the iframe's src URL.
I made the widget keeping mobile users in mind, however it suits both mobile and desktop. If you run into issues, leave a comment here. I have attached some screenshots of the content of the iframe here.