Generate sample of a random process with given correlation function

Question

My task is in numerical modeling evolution of a random quantity. For this, I need first to generate a multitude of sample sequences that correspond to a predefined correlation function. In other words, considering the process $a(\mathbf{x})$ is a function of N-dimensional vector $\mathbf{x}=(x_1,\ldots,x_N)$ and supposing its stationarity, i.e. $\langle{}a^{\ast}(\mathbf{x}')a(\mathbf{x}'')\rangle=K(\mathbf{x}''-\mathbf{x}')$, which way can I generate random samples of $a(\mathbf{x})$ that obey $K(\mathbf{x}''-\mathbf{x}')$ ?