Working Solution December 14, 2020
For simple usage like 3rd party tools that require an Instagram user ID (like embedding an image feed) I tend to use:
https://www.thekeygram.com/find-instagram-user-id/
because it makes it really easy to copy and paste the Instagram user ID that I am looking for. Unlike most tools I get the results fast, it's free and there are no ads. I recommend you watch the youtube video before using it so you can see how simple it is and get an idea of how it's used:
https://www.youtube.com/watch?v=9HvOroY-YBw
For more advanced usage I recommend:
https://www.instagram.com/{username}/?__a=1
(replace username with the requested username)
For example to find the user ID of the username "instagram" you would use:
https://www.instagram.com/instagram/?__a=1
This is the most advanced way which returns a JSON response and it's great if you are building an app that requires the raw data. You can save it in a database or build some type of front end UI to display it. Example: for a dashboard or on a website. Also, using the url is great because you can get additional attributes about users such as their total follower count and profile bio.