Gourmets, also known as Mouthers, like to play with the nipple and taste the milk before digging in. If hurried, they scream in protest, but once these gourmands find the milk to their liking, they settle down and nurse well.
How to Help Them
Don't rush. Yes, nipple-fingering and mouthing make breastfeeding in public difficult to do discreetly, but it also stimulates your hormones and encourages milk production. So even if you want to say "Drink it already!" take a breath and let him do his thing.
Insist on a proper latch. When your baby finally starts sucking, you'll be tempted not to disturb him even if his latch isn't right. Make yourself do it anyway. (Check out the latch-on advice under "Barracudas.")
Enjoy it. Grab a magazine or a book -- or simply watch and giggle at this little nurser's lip-smacking and tongue-wagging -- and try to relax.