Breastmilk production is divided into two stages, it starts out as hormone driven and then switches over to a supply and demand system.
During pregnancy a combination of various hormones trigger the mother's breasts to start making milk (colostrum) but the high levels of the progesterone hormone limits the volume/amount of milk being made to only a small amount and also keeps the milk in the breasts.
Your body will always make perfect milk, tailor made for your little one's specific needs.
When the placenta is delivered at birth (Natural, C-section, the way doesn't matter), the levels of progesterone suddenly drops, thus the little progesterone security guard that kept the milk inside your breast and made sure the volume stayed small is now gone. Now there is no-one limiting your breasts' milk factory and your breasts start to increase the amount of milk and also start letting milk out. Between day 3 to 5 you feel your mature "milk come in" and breastfeeding and milk production is really taking off.
Don't worry if your mature milk takes longer to come in. The colostrum milk that you are making in the beginning is like a super milk. Because your body knows that your baby's tummy can only take 5ml per feed, your body creates this super milk to pack in all the nutrients and goodness in a concentrated form. 5ml of colostrum is so good that it is equal to quite a bigger amount of "mature milk" in terms of nutrients.
Once your mature milk comes in, your milk production works on the supply and demand method. As long as there is a demand, meaning the breasts get emptied, your breasts will keep producing more milk to replenish the warehouse.Thus the more your baby nurses, the more milk gets made to keep up with the demand.
Doing lots of skin-to-skin with your baby and smelling them close, will also aid in your milk production and can help your milk come in faster.
Now you may wonder what actually goes on in the milk factory to make the milk? Inside your breast are alveoli, these look like little trees with branches and the roots lead to your nipple. The milk is made in the fruit on the trees, called lactocytes (milk-producing cells on the alveoli). These "fruit" (lactocytes) are prolactin receptor sites that allow the prolactin in your blood, to enter them and then the synthesis of breastmilk happens. Prolactin is a hormone produced by your pituitary gland that prompts your lactocytes to filter proteins, sugars and fats from your bloodstream to make milk.
Then the "trees" (alveoli) are full of milk, the "trees" and "fruit" (lactocytes) stretch and expand, also changing the shape of the "fruit" so that no more prolactin from your blood can enter the "fruit" to make more milk. When the breasts are emptied, the "trees" and "fruit" return to normal shape and size and the prolactin from your blood can enter the "fruit" again so that more milk can be made.
You can thus gather that breastmilk is made from your blood, not your stomach content, thus what you eat will not usually affect your baby, unless your baby is allergic or sensitive to something specific. All foods are safe while breastfeeding if consumed in moderation (meaning don't eat only one food, all day, for a week).
You also don't need to follow a specific diet to make good milk. Your body will always make perfect milk, tailor made for your little one's specific needs. Even if mom is following a really unhealthy lifestyle, her body will produce healthy milk and if a mom's diet is lacking in a certain vitamin that is needed, her body will search within her body for a fat cell to use that contains that specific vitamin that is needed, from years ago when she ate eg. a bite of steak and the nutrient was stored in that fat call for years and years. Even mothers living in very poor countries and poverty produce healthy milk.
During each nursing session, your breasts' glands also analyses your baby's saliva and will adapt your milk to her needs. If she is sick, your body will create antibodies and give it to her via your milk. Also if mom is sick, her body creates antibodies to give to baby to protect her from the illness. Even when mom is in contact with other ill people or someone sneezes near her, her body will respond to create antibodies to protect her baby via her breastmilk. This is why it is also very important for mom to continue nursing when she is sick.
Your breasts are also never ever empty, as it produces milk on the 80/20 ratio. This means that they always produce enough milk to maintain the ratio of 80% of milk is what your baby always drink and 20% extra for just in case. So if your baby has grown over night and needs more milk or for any reason needs more milk and drinks from the extra "20", your body increases production to maintain the ratio.
One thing you need to keep in mind also is the storage capacity of your breasts, which is in no way related to breast size. The amount of "trees" (alveoli) a woman has in her breast varies and thus if you have a small storage capacity, your baby will need to need more often to get the amount of milk she needs.
This means a mom with big breasts can still have a small storage capacity and a mom with small breasts can have a very large storage capacity (milk factory).
Regardless, babies nurse for more reasons than just hunger and it is important to let baby nurse for both hunger and nurture.