Don't be surprised to find yourself on the receiving end of one of your baby's left hooks, though she's not likely to give you a black eye just yet. As a newborn, her hands will be curled up tightly into tiny fists, and because she doesn't have much muscle control, her movements will be jerky and awkward. Over the next few weeks, however, this will start to change. Your baby will gain the ability to open and close her hands and to grip objects pressed into her palm, such as a rattle or your finger.
As she nears 3, then 4, months, you'll notice her using her whole palm with her thumb parallel to the rest of her fingers to grab objects. This grip might not be efficient, but she'll get better with time.
As her coordination improves, her hand and arm movements will become more refined and less reflexive. Give her opportunity to practice these skills, but if your baby's unsuccessful swats frustrate her, take a break from the activity.