Have you ever seen ticket machines located in the front of ramen restaurants? You use this machine to buy a ticket for ramen and toppings. After you are seated, you hand the ticket to the chef and they will start preparing your order.
After sitting down at the counter, talk to the chef directly to place your order. In this case, you pay at the register after you eat. If they slip you a receipt while you are eating, bring it to the register too.
After You Eat:
Ramen in Japan is considered fast food. Therefore, you should not be at a ramen restaurant for too long. It is better to leave right after you finish eating.