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We describe in detail how to implement a coarse-grained hybrid Molecular Dynamics and Stochastic Rotation Dynamics simulation technique that captures the combined effects of Brownian and hydrodynamic forces in colloidal suspensions. The importance of carefully tuning the simulation parameters to correctly resolve the multiple time and length-scales of this problem is emphasised[1,2]. Applications to be discussed include: The effect of hydrodynamics and Brownian fluctuations on percolation and aggregation, the sedimentation of colloidal particles, dynamic lane formation in driven suspensions, and the direct simulation of a microfluidic nano-pump. [1] Hydrodynamic interactions and Brownian forces in colloidal suspensions: Coarse-graining over time and length-scales, J.T. Padding and A.A. Louis, Phys. Rev. E 74, 031402 (2006) [2] Hydrodynamic and Brownian Fluctuations in Sedimenting Suspensions J.T. Padding and A. A. Louis, Phys. Rev. Lett. 93, 220601 (2004)