When it comes to ordering at ramen (or other noodle or fast-food) restaurants, there are generally two methods.
The first is through ticket machines, often found at the entrance or right outside the store. Simply decide on the ramen you want from the menu, insert your money, and press the button for the corresponding dish. Take the ticket and hand it to the waiter or place it on the counter for the cook to see.
The second method is similar to any other restaurant in Japan–order after being seated. If you’re unsure how to say the ramen name in Japanese, just point to the picture on the menu and you should be good to go.
Bon appetit!