Information flow between the systems can be quantified by using the measures that are derived from entropies by observing the state variables. In this study, the mutual information and the transfer entropy of the coupled Gaussian processes and the entropy of the bistable system have been estimated for this purpose. Information measures of the systems have been obtained by the histogram, kernel density estimator, k-nearest neighbor entropy estimator and kpN entropy estimator for the different parameters. Normalized bias and normalized standard error have been calculated to determine the performance of the estimation of the entropy measures. The optimal parameters of the entropy estimators of information measures have been obtained. It is shown that k-nearest neighbor entropy estimator has the best performance for the coupled Gaussian processes. Additionally, the entropy of a nonlinear system i.e. the bistable system has been estimated. While kernel density estimator and k-nearest neighbor entropy estimator have succeeded in achieving the estimation of the entropy in the bistable system, it is shown that normalized bias and normalized standard error of histogram and k-nearest neighbor method have high ratios. The entropy estimations of the coupled dynamical systems have been estimated with considerable accuracy when the optimal parameters of the entropy estimations have been used. The transfer entropy of a real dataset has also been estimated via these methods. We have discussed the statistical significance of the estimation methods of transfer entropy by using a hypothesis test. The study provides a way to determine information measures that quantify the uncertainty of the systems and information flows between the systems, accurately.