Spreading of a viscous fluid droplet on a solid surface is studied using a horizontal solid-on-solid model, with Langevin theory for the two-dimensional case and the Monte Carlo method for the two- and three-dimensional cases. The substrate interaction with the droplet is described first with one-monolayer-range chemical potential and second with a long-range van der Waals–type potential. Partial- and complete-wetting regimes have been studied by investigating dynamic droplet profiles, spreading speed, contact angle, and their characteristic time behaviors. The change from partial to complete wetting happens when the total interaction of the substrate with the droplet exceeds the interatomic interaction between fluid particles. The thickness and speed of the precursor film depend on the value and range of the substrate potential.