This is true for any continuous distribution and not just a normal. You simply calculate the sample standard deviation and divide it by the square root of n.
Let m be the the mean for the sample sum the squared deviations of the observations Xi for the sample mean m divide by n-1 (of the unbiased variance estimate) and take the square root for the sample standard deviation estimate. Then divide by the square root of n to get thestandardthe standard error.