I nurse in public all of the time now but I was so nervous when I first had to. My saving grace has been baby wearing. When my son starts pulling at my shirt, I put him in a baby carrier (or, if he already in it, just move my shirt) and let him nurse away. No one has really been able to tell (to my knowledge) but I also bring a light hooded sweatshirt, cardigan, or front tie cover up to wear if I want extra privacy.
I've nursed at parks, at restaurants, on airplanes, in stores, at festivals, at a pool etc. I usually feel more comfortable when I'm around other moms but, that being said, I've only even gotten positive comments from strangers while nursing. When not in a carrier, my son just pulls my nursing cover off, so I either use the cover to sort of block the view without putting it over him or I just pull one side of my hoodie/sweater/etc to block anyone's views if I feel nervous about nursing in a super crowded place.