A number of resources I found useful while learning about copulas.
NC State University lecture notes - A consise introduction into copulas. This is a good place to start but not a good place to find examples.
Copulas for Finance: A Reading Guide and Some Applications - A much more intense survey of copulas. Math heavy but full of examples. Page 20 includes a few simulation techniques, but overcomplicates the simple ones (Gaussian copula) in order to stay general.
Wiki: Copulas - The mathematical definition section, along with Sklar’s theorem and the section of Gaussian Copulas makes this worthwhile to look at.
StackExchange answer - This was the missing link for me. A great description of the “point of a copula.” The full explanation in the last paragraph of the answer made things click for me.
DataScience+ - A good walkthrough of using the copula R package. Includes an example of using a t-copula with normal marginals.
copula - The copula R package. A one stop shop for your copula needs if you use R and don’t want to (or have to) implement it all yourself.
Matlab example - Obviously the code is all in matlab, but they do a nice job of explaining how to simulate from copulas, without the theory.