Computers these days make special effects easy. But back in Young Frankenstein's time, they had to be a little more creative. They had to create trick candles, fog, rain, electricity, and actually bring a dead body back to life in order to make everything look real on the big screen. No CGI monsters were available.
Brooks couldn't have done it without Gerald Hirschfeld, a cinematographer who worked on black-and-white and color movies. Even though Hirschfeld was on the front lines when the industry changed to glorious Technicolor, this man still appreciated the nuances of black-and-white photography. He said, "if it's right for a story to be photographed in black and white we shouldn't arbitrarily shoot it in color." So once Brooks won the fight to film Young Frankenstein in shades of gray, Hirschfeld was the perfect choice. And especially with many of the original film's sets, B/W was the perfect choice, too.
Oh, and get this: the lab equipment they used was apparently some of the original equipment used in the 1931 Frankenstein movie and its sequels (source). Talk about upholding a legacy.