This article may guide you a little.
As always, remember that you can be guided in more detail on the official sites:
There are plug-ins available if you’ve paid for a business version of WordPress. (https://wordpress.org/plugins/duracelltomi-google-tag-manager/)
However, if you’d rather do it manually, it’s relatively simple to do. It will only get tedious if you have a ton of different pages of your site and want to use tags on all of them -- you’ll have to copy and paste a code below the <body> tag on each page.
Here’s what you do:
1. Copy your tag code.
Copy the Google Tag Manager code you are given during the set-up process. If you’ve already set up your account, click the blue “Google Tag Manager” code beside “Workspace Changes” on your Google Tag Manager homepage (circled below in red). That blue code will also supply you with your specific Google Tag Manager code.
2. Install the code in WordPress.
Now, paste that code below the <body> tag of each page on your WordPress site.
Now, your WordPress site is prepped for any tags you want to create within Google Tag Manager. Google Tag Manager will automatically code future tags and embed them on whichever page you’ve selected.