Premature birth is when a baby is born before 37 weeks. Prematurity often will mean that the baby is born at a low birth weight, defined as less than 5½ pounds. When a baby is born early or is small at birth, the mother and baby will face added challenges with breastfeeding and may need to adjust, especially if the baby has to stay in the hospital for extra care. But keep in mind that breastmilk has been shown to help premature babies grow and stay healthy.

Some babies can breastfeed right away. This may be true if your baby was born at a low birth weight but after 37 weeks. These babies will need more skin-to-skin contact to help keep warm. These smaller babies may also need more frequent feedings, and they may get sleepier during those feedings.

If your baby is born prematurely and you are not able to breastfeed at first, you can:

• Express colostrum by hand or pump in the hospital as soon as you are able
• Talk to the hospital staff about renting an electric pump. Call your insurance company or the local WIC office to find out if you can get refunded for this type of pump. Under the Affordable Care Act, most insurance plans must cover breast pumps, but your plan will tell you if you are able to rent an electric pump or a manual pump.
• Pump milk as often as you would normally breastfeed — around eight times in a 24-hour period.
• Give your baby skin-to-skin contact once your baby is ready to breastfeed directly. This can be very calming and a great start to your first feeding. Be sure to work with a lactation consultant on proper latch and positioning. It may take some time for you and your baby to get into a good routine.

source: http://www.womenshealth.gov