In the newborn stage, while you are still working on establishing breastfeeding, pain is not all that unusual bit it should not exceed more than mild discomfort. If your baby has not latched on properly, it can hurt. Your nipples can be sore in the early days, which you can remedy with creams like lanolin or even cabbage leaves help. It is also possible to get a plugged milk duct which can cause you some pain. This can be resolved by plenty of breastfeeding, pumping, or massaging, directed towards the painful area. Some of the things that cause pain during breastfeeding are harmless and go away soon enough, as you can see. But some of the more serious problems are thrush (a fungal infection that can appear on your nipples and in your baby's mouth), and mastitis. For more information on what to do if you get this, look at how to beat mastitis.
A strong let down, engorged breasts, and even a badly fitting bra can also induce a fair bit of pain. The first will probably go away with time, engorged breasts can be cured with breastfeeding, and a badly fitting bra is not difficult to throw away! I was a breastfeeding mother for four years in total and I have to say that I have never had any problems beyond sore nipples while breastfeeding in the first few days after my babies were born. If you're reading any article about breastfeeding problems (including this one!), it might all sound really scary. Breastfeeding does not generally hurt at all in my experience, and neither is it difficult. That's something worth saying, because it is easy to give up when you think it will be terribly hard. Prepare for breastfeeding problems if you want to, but don't expect to have them in advance.