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We discuss the effect of the dielectric environment (insulators and metal gates) on electronic transport in two-dimensional (2D) transition metal dichalcogenides (TMD) monolayers. We employ well-known ab initio methods to calculate the low-field carrier mobility in free-standing layers and use the dielectric continuum approximation to extend our study to layers in double-gate structures, including the effects of dielectric screening of the electron-phonon interaction caused by the bottom oxide and the gate insulator, and of scattering with hybrid interface optical-phonon/plasmon excitations (`remote phonon scattering'). We find that the presence of insulators with a high dielectric constant may improve significantly the carrier mobility. However, scattering with the interface hybrid excitations negates this gain and degrades the mobility significantly below its free-standing value. In a double-gate geometry with SiO$_{2}$ as bottom-oxide and various top-gate insulators, we find that the mobility decreases as the top-insulator dielectric constant increases, as expected. However, a high mobility is predicted in the case of the weakly polar hBN, and a mobility much lower than expected is calculated in the case of gate-insulator/TMD/bottom-oxide stacks in which two or more polar materials have optical-phonon with similar resonating frequencies. We also find that the effect of screening by metal gates is noticeable but not particularly strong. Finally, we discuss the effect of the TMD dielectric constant, of the free-carrier density, and of temperature on the transport properties of TMD monolayers.