When will my baby be able to grab?

At birth... The "grasp reflex" (closing the fist around something placed in it) should be present at birth. "rake grasp" (reaching for an object successfully) by 4-6 mo, "pincer grasp" (thumb and forefinger) by 9-12 months.
Three to four months. Usually babies will start to reach for things at three to four months with progressive refinement of movements. By 9-10 months babies should be able to use a pincer grasp using opposing thumb and forefinger to grab.