Breastfeeding: How it works

The simplest explanation in my own words. Hope it helps. :)

Milk Glands - make milk. Then milk travels through this glands to milk ducts. These milk ducts then widens into several milk sinuses. Through this milk sinuses, milk will come out to many openings at the nipples.
Baby's sucking sends message to the pituitary gland to secrete prolactin. Prolactin surges stimulates milk production. Continued sucking also releases hormone oxytocin. This hormone sends out  large amount of milk at once. This is called Milk Ejection Reflux (MER). The system works the same with pump stimulation. You can see milk squirting in all directions when you pump.

IMPORTANT: It is usually the time in between the first few sucks (till milk decreases to few drops) and the continued sucking to secrete prolactin, where baby fidgets (or pump shows no more milk). Usually this is when everyone ASSUMES all kinds of things (less milk/no milk etc) and give up on breastfeeding. You just need to continue for another 2-3 minutes to trigger prolactin and to see milk flowing again and baby will suck properly again.

                       
Another tip: Keep feeding every 2 hours. For some, you may need to feed every 30 minutes in the beginning. Just keep going on, things will get easier. You and baby can learn a lot with frequent feeding.
The more milk you remove from your breasts, the more it will produce.
Option: You may empty your breasts after each feed via pump or even pump before your feed. When you tell your body that your baby's demand is high, your body produces enough supply to fulfill it.