They'll be pinker or redder than usual, itchy, possibly flakey dry skin. And the pain will get worse - especially during letdowns. And the same pain will be there when pumping.
My nipples were pink and a little itchy. But for me, it was the unmistakable pain. It became so bad that I felt like I was going to pass out. Like shards of glass. I caught it faster the second time around.
I've had both mastitis and thrush. With mastitis, I was sore and miserable whether I was nursing or not and also felt full body aches. With thrush, I only felt terrible while nursing, like I had crushed glass inside my nipple every time the baby sucked. It didn't start looking any different until I'd already had it for a day or two.