Google's Tag Manager service allows you quickly and easily update various measurement tools on your site without having to implement new scripts in the code for each service.
To implement Google Tag Manager on your website, you'll need to install their "container" code inside the <head> and <body> tags of your site. Detailed instructions from Google can be found here.
You can add your Google Analytics account to your Google Tag Manager account to track e-commerce activity via Tag Manager.
Once your GTM container code is set up, and Analytics is set up in GTM, you'll need to add Tags in GTM to track various e-commerce events, such as a customer checkout.
In Google Tag Manager, you'll need to create a new Tag. It should be a Universal Analytics tag with a Track Type of "Transaction". The Tag will need a Trigger, too. Set up a trigger based on a Custom Event called "transactionComplete". **The name and capitalization of this event is very important.**
That's it! It's always good to place a test transaction and check in Google Analytics to verify that the install is successful.