There are two ways to find your podcast's iTunes ID:
1. Through the iTunes desktop application
Open iTunes on your computer and browse to your podcast's page in the iTunes Store. The easiest way to get there is to search for it's name. Once on the page, you will find a button labeled Subscribe on the left side. Click the down arrow and then Copy Link to copy your podcast's store URL.
Paste the URL into a text editor or word processor. The ID is only the last numerical part of the URL (marked in the image below).
2. Through Apple's Podcasts Connect platform
Go to https://podcastsconnect.apple.com and log in with your Apple ID. Click on the podcast cover of the podcast in question. There you will find the so called Mirror URL. The podcast's ID is only the last numerical part of this URL (marked in the image below).