There are times when a business gives away free products or the checkout has a total amount of zero dollars after giving away discounts, coupons, etc. and you don't want to ask the customer's payment information (e.g. credit card number) to increase registration and checkout conversion.
You can do so by enabling the special None payment method from Configuration > Payment methods menu. The None payment method will bypass taking payment and allows the checkout to complete successfully. However, you want to make sure to allow this payment method only if the conditions are met (zero amount) and not accidentally bypass payment for a valid paying order.
To do so, you need to set the Availability rule for the None payment method so that it only becomes available when the minimum and maximum amount or balance is exactly zero.
Likewise, you may want to do the reverse for the other payment methods (credit card, etc.) and set the Availability rule to allow only when the minimum amount or balance is greater than zero. This may or may not be the case for your business because you may want to give a free recurring product on the first month but you also want to offer the customer to the opportunity to enter their credit card information for taking next payments (first month free, and $20 thereafter charged to the credit card).