First of all, congratulations on your recent new child, and congratulations on deciding to breast feed! Breast feeding is the best way to feed your child, as it provides bonding time for you and your baby and also provides your baby with important antibodies and other substances not found in formula milk.
Tender breasts are a common problem for many breastfeeding mothers. Fortunately it is a problem that can usually be corrected with some simple techniques.
First of all, improper positioning of the baby while breastfeeding causes tugging on the nipples which is painful. Make sure the baby is well positioned, not dragging down on the nipple, and with the entire nipple and surrounding dark area in its mouth.
Second, if you have any chafing or cracking of the nipple itself, consider wearing nipple shields inside your bra to minimize this. Also, make sure to gently dry your nipples after breastfeeding to prevent skin breakdown, and consider a thick moisturizing agent like vaseline (make sure to wipe off before breastfeeding).
If these strategies do not work, there are additional resources available to you. You could start by talking with your obstetrician; they may be able to recommend a lactation expert to help you work through these difficulties.