There are few different methods to test the WooCommerce Checkout process without the use of 3rd party plugins.
100% Coupon
Create a coupon code with a 100% discount. This can be applied during checkout to complete the process. Refer to the WooDoc for Coupon Management.
Enable Check Payments
Enabling check payments will complete the checkout process without requiring online payment. Orders using Check Payments are set On Hold until payment clears outside of WooCommerce. Refer to the WooDoc for enabling Check Payments.
Cash on Delivery
Cash on Delivery (COD) is a payment gateway that required no payment be made online. Orders using Cash on Delivery are set to Processing until payment is made upon delivery of the order by you or your shipping method. Refer to the WooDoc for Cash on Delivery.