If a dog has conjunctivitis will it be contagious to a human?

It depends, conjunctivitis can be caused by a virus, bacterium or just an allergic reaction. The contagiousness of the first two depends on the strain of infection the latter wouldn't be transferable.

Normal sanitary precautions should prevent spread. Wash hands in hot soapy water after touching the dog and before you touch your face.

I had a dog with conjunctivitis and took him to the vet to get steroid eye creams to decrease the inflation, and antibiotics to combat infection. It is easy to train a dog to accept eye drops by using lots of positive reinforcement, a soothing voice and a nice reward (my dog liked ham). He was a breed prone to this condition so as a prophylactic measure we used moisturising non medicated eye drops thereafter, which decreased the number of infections. I never contracted conjunctivitis from him.