I know that for the $2$-dimensional case: given a correlation $\rho$ you can generate the first and second values, $ X_1 $ and $X_2$, from the standard normal distribution. Then from there make $X_3$ a linear combination of the two $X_3 = \rho X_1 + \sqrt{1-\rho^2}\,X_2$ then take $$ Y_1 = \mu_1 + \sigma_1 X_1, \quad Y_2 = \mu_2 + \sigma_2 X_3$$

So that now $Y_1$ and $Y_2$ have correlation $\rho$.

How would this be scaled to $n$ variables? With the condition that the end variables satisfy a given correlation matrix? I'm guessing at least n variables will need to be generated then a reassignment through a linear combination of them all will be required... but I'm not sure how to approach it.