In my opinion, Ichiran is second to none when it comes to the best ramen in Japan. There are branches all around the country but if you visit Kyoto, the Shijogawaramachi branch may be the most convenient to you as it's located in a shopping area near Gion.
Entering the restaurant, you are required buy a ticket from a vending machine. At that moment, you have to decide on the quantity of ramen and side dishes you would like to try. Subsequently, you will be led to a booth where you are supposed to enjoy the food individually. A cordial waiter will give you an order form in which you can choose the texture of the ramen, thickness of the soup, amount of hot sauce, etc. Don't be turned down at this point if you are not a lonely patron. The partition of each booth can be removed, so you can still chat with your friends while eating. Drinking all the soup is a gesture of courtesy but it's still ok not to do so as it can be quite salty.