We consider the diffusion of innovation in two-sided markets where both sides choose between an incumbent technology and an innovation. Each player chooses whether to adopt the innovation or not, and repeatedly learns how many players on the other side of the market adopted the innovation and revises her decision accordingly. Using large-system analysis, we characterize the dynamics of the market, and show a phase transition result: If the initial proportion of adoptors on both sides are sufficiently large, then the innovation will spread to the entire market; otherwise, no one will adopt the innovation. Assuming the innovator can select the proportion of initial adoptors on both sides of the market by advertisements, we study the following three economic problems that are of interest to the innovator: 1) minimizing the advertisement cost while allowing the innovation to spread, 2) minimizing the total cost of advertising and technology improvement while allowing the innovation to spread, and 3) maximizing the total revenue less advertisement cost, where the innovator derives revenue per unit time from each player adopting the innovation. Our analysis provides insight into the types of advertising strategies that can lead to the successful adoption of an innovation.