Merchants located in the United States and on either the professional or enterprise plans of Recurly have access to ACH processing.
To begin processing ACH transactions via Recurly you would need apply for a Check Commerce account. To do this you can go under configuration -> payment gateways, from there you can select add payment gateway then select Check Commerce. From that page look at the box on the right had side labeled "Need an account" and click on the button "request an account" to apply for a check commerce account. (You will be redirected to Check Commerce's online application for a new account.)
Once you are approved for a Check Commerce account, you can use the credentials provided by Check Commerce to connect your account to your Recurly site. You can do this by going back under under configuration -> payment gateways, from there you can select add payment gateway then select Check Commerce. From that page you can enter in your Check Commerce Merchant ID (a numeric string) and Password, select the box "enabled for new transactions" and hit add payment gateway. Once you do that you will see Check Commerce listed under the list of your payment gateways.
Now that you have Check Commerce enabled for ACH, you will need to configure your payment forms to include the "Bank Account" option. If you are using the hosted pages the ACH option would appear automatically at this step however if you are using a custom form via the API and Recurly.js you would need to make the needed adjustments to add the option to collect ACH information.