Add more variables to the model. One method of reducing the root mean square error is to make a more complex model. While more complex models always fit the data better, the value of this better fit must be weighed against the added complexity.
Add transformations of the variables to the model. For example, if you are modelling weight as a function of height in adult humans, it will reduce root mean square error if you add height squared to the model. However, the same cautions apply regarding complexity of the model.
Get more accurate data. If you can measure your variables more precisely, then this will reduce root mean square error. Part of the error that is measured by RMSE is due to inaccuracies of the model; no model is perfect. But any inaccuracy in measurement will also add to the error.