How and where do I paste structured markup data on my wordpresswebiste?

Are you trying to add structured data like name, address, phone number, etc.?
If so you can easily add that code to a widget anywhere on your site.
To check that you have everything setup correctly you can use the Structured Data Testing Tool.
There are sites that will help generate the correct code if you think you might have something wrong like https://schema-creator.org/ or https://www.microdatagenerator.com/
There are plugins that will help generate code for you as well.

Ok. Thank you. I thought it needed to be exactly where Google’s structured data markup tool showed it to be.

What do I need to add so the markup data doesn’t show on the published page?

If you go to one of the online generators they will provide you with all the code you need, which can be copied/pasted into a regular text widget. The code format would look something like this:

<div itemscope itemtype="https://schema.org/LocalBusiness">
   <span itemprop="name">Some Business Name</span>
   <div itemprop="address" itemscope itemtype="https://schema.org/PostalAddress">
     <span itemprop="streetAddress">123 Main St</span>
     <span itemprop="addressLocality">Anytown</span>,
     <span itemprop="addressRegion">AZ</span>
     <span itemprop="postalCode">85795</span>
   </div>
   Phone: <span itemprop="telephone">555-555-5555</span>
</div>

but it wouldn’t have all that code when reading it on the live version of the site, like this:
Some Business Name
123 Main St
Anytown, AZ 85795
Phone: 555-555-5555

The generators could produce other information depending on the type of business you have, but this is a basic example of what I think you’re looking for.

Mahalo Scott! ??