If she's falling asleep once she's full and satisfied, that's fine. However, if she is having trouble staying awake to eat for at least 10 to 15 minutes, you'll need to try a few tactics to wake her.
A baby falling asleep early in feedings can be a sign of a shallow latch, which causes a milk flow so slow that baby quickly loses interest. The solution is to latch baby on deeper.
If baby's latch is good and she's just plain sleepy, skin-on-skin contact can sometimes help; remove your top and bra as well as your baby's clothes (but leave the diaper on), and lay her on your chest. This may stimulate her enough to keep her nursing. Other moms swear by tickling their babies' feet, stroking their legs, or jiggling their arms and legs to keep them awake and sucking.
Some experts recommend a strategy called "switch nursing" — when baby starts nodding off, take her off the breast, stimulate her (hold her upright, talk to her, tickle her, rub her, burp her), and offer the other breast. Repeat this scenario until she's logged at least a good 10 to 15 minutes of feeding.
Another strategy is to try breast compressions, a tactic popularized by Canadian pediatrician Jack Newman.