The two processes you should know
In general, ramen stores have two distinct ways of ordering. Some stores have ticket machines at the entrance or outside the store. By looking at the menu, you should pick a ramen that you like, insert the money and press the botton with the ramen that corresponds to the one want to try. Then, bring the ticket inside the store and give it to the waiter or put it on the counter for the cook to see.
The other way is similar to any other restaurant in Japan, in which you order after you are seated. If you don't know how to say the ramen you want in Japanese, you can point to the picture on the menu to make sure that the waiter understands what you want. This way, the process of ordering will go very smoothly!