You get an extension ID when you upload your extension to Google Web Store. Ie. Adblock has URL https://chrome.google.com/webstore/detail/cfhdojbkjhnklbpkdaibdccddilifddb and the last part of this URL is its extension ID cfhdojbkjhnklbpkdaibdccddilifddb.
If you wish to read installed extension IDs from your extension, check out the managment module. chrome.management.getAll allows to fetch information about all installed extensions.
If you just need to do it one-off, navigate to chrome://extensions. Enable Developer Mode at upper right. The ID will be shown in the box for each extension.
Or, if you're working on developing a userscript or extension, purposefully throw an error. Look in the javascript console, and the ID will be there, on the right side of the console, in the line describing the error.
Lastly, you can look in your chrome extensions directory; it stores extensions in directories named by the ID. This is the worst choice, as you'd have extension IDs, and have to read each manifest.json to figure out which ID was the right one. But if you just installed something, you can also just sort by creation date, and the newest extension directory will be the ID you want.