Incorporating the individual and collective problem solving skills of non-experts into the scientific discovery process could potentially accelerate the advancement of science. This paper discusses the design process used for Foldit, a multiplayer online biochemistry game that presents players with computationally difficult protein folding problems in the form of puzzles, allowing ordinary players to gain expertise and help solve these problems. The principle challenge of designing such scientific discovery games is harnessing the enormous collective problem-solving potential of the game playing population, who have not been previously introduced to the specific problem, or, often, the entire scientific discipline. To address this challenge, we took an iterative approach to designing the game, incorporating feedback from players and biochemical experts alike. Feedback was gathered both before and after releasing the game, to create the rules, interactions, and visualizations in Foldit that maximize contributions from game players. We present several examples of how this approach guided the game's design, and allowed us to improve both the quality of the gameplay and the application of player problem-solving.