Usually if there is nowhere completely private you can find somewhere away from the crowds, such as an out of the way bench at the park or on a blanket behind a big tree. Some moms will go to their cars and use a sunscreen in the windshield for privacy or park in a distance spot. In restaurants the booth in the back corner works well, just make sure you are facing the wall and the others with you face out. At a family gathering you can usually slip off to a more private place in the house. In church sit in the back pew, others should be facing front and you will be too far away for the clergy person to see you clearly.
Some moms are most comfortable using a bottle of expressed breastmilk when in public.
In my opinion, this option is not as easy and involves a lot of preplanning. Try to feed your baby at the first sign of hunger, since a crying baby will draw attention. Also recognize that a quiet breastfeeding baby draws less attention and is less disturbing to most people, than one who is crying to be fed but is being asked to wait because mom doesn't want to be seen breastfeeding in public. As your baby gets older he or she will take longer stretches of time between feedings, so it often becomes possible to time outings between feedings. Moms who are comfortable breastfeeding in public areas should not be discouraged from doing so.