See also the StopTheScript macOS and iOS support pages for more information.
After downloading StopTheScript from the App Store, you need to check the checkbox in Safari Settings to enable the extension.

If desired, check the checkbox to allow the extension in private browsing too.

A common mistake is to allow StopTheScript on every website. You probably don't want that! Allowing StopTheScript on every website stops JavaScript on every website, which would cause a massive amount of breakage. Instead, allow StopTheScript only on websites where you know that you need to stop JavaScript.

Below is an example of an annoying website that is improved by stopping JavaScript. Notice that the popup prevents you from reading the news story.
To allow StopTheScript on the website, click the StopTheScript icon in the window toolbar.

Clicking the toolbar icon opens a permissions popup. Again, a common mistake is to select Always Allow on Every Website. Don't do that! Instead, select Always Allow on This Website.

The StopTheScript toolbar icon is now tinted, which indicates that it has permission to access the website. The first time after you allow the extension on a website, you need to reload the page to stop JavaScript.

As you can see below, JavaScript is now disabled.
In most cases, that's sufficient to eliminate website annoyances. In this case, however, it's not sufficient. (I chose this example on purpose to illustrate all of StopTheScript's features.)

The web page has an HTML noscript element that displays when JavaScript is disabled, and this still obscures the news story.
By default, StopTheScript shows noscript elements. If you want to hide them on a website, click the extension toolbar icon to open its popup window.

Add the website, using its full domain, and uncheck the Show checkbox to hide noscript elements on the website.

Now if you reload the page once more, the news story is no longer obscured!

You can scroll down the page to read the entire story.

If you open Safari Extensions Settings again, you can see that the extension is now allowed on that specific website.

This is also shown in Safari Websites Settings, where you can edit the extension's website access if necessary.

Note that the extension is set to Allow only for specific websites and set to Ask for other websites.
The workflow is essentially the same on iOS as on macOS.