having tried many methods over the years, by far and away the best method bar compression clothing that HJ suggests (that's fine in winter but too hot in summer) is to use some tape called Strappal. this is the tape used by physios to strap sports injuries and is stickier than sticky stuff so stays put whereas lesser tape will sweat off.
you can get it in 1cm width and it tears off (fabric backed) so easy to apply. and a bugger to get off if you have a hairy chest like mine! but I'll take a small amount of hair tearing than shredded nips any day
the other good product is Nipguards but they are very expensive in comparison to Strappal