Sprint has sprinted to the update process for the Samsung Galaxy S III faster than any another other U.S. carrier and will start pushing out the update for Android 4.1.1 Jelly Bean later today. This update will seem like it just drops into to Samsung Galaxy S III, however we'd like to remind to try not to drop your S3 on the ground or into the pool (see what happens).
Typically over-the-air (OTA) updates start slowly at first and then are sent out in bigger numbers over time, especially over the weekend. When your Samsung is eligible for the update, it will download automatically.