Remember that the power spectral density (PSD) of anything is the Fourier transform of the autocorrelation function of that process.
Hence, if you want a defined autocorrelation function (ACF), do its inverse Fourier transform, and you'll get a PSD that would represent a signal of given ACF.
Now, you can use all the beautiful methods of filter design to come up with a filter that, when applied to a white process (e.g. random numbers from a random number generator) will shape that process's PSD as desired!
So, that's kind of the general look at things: If you just want something like
"Each sample should be correlated much with the previous one, but only slightly with the one before"
then maybe understanding it as roughly
$$y[n] = 0.9x[n] - 0.1x[n-1]$$
would get you there quicker: $(0.9, 0.1)$ is actually the coefficient vector of a FIR filter that you can apply to your uncorrelated input vector $x$ and be done with it.