How can I generate random observations from a concrete copula? Let us assume that we have two continuous random variables $X$, $Y$, with known distributions (not necessarily normal), connected/related via a concrete copula.
What is a procedure to generate random values from this pair $(X,Y)$?
For a single random variable $X$, I usually generate (pseudo)random values within $[0,1]$ and then transform them into observations of $X$ using its inverse-CDF. Can I do the same when I have copulas?
I am asking for a generic procedure/recipe.

A recipe for how to generate random observations depends on the level of detail. If you can generate from the copula, then you get points on $[0,1]\times [0,1]$. Then you transform the $X$ coordinate into $X$ and the $Y$ coordinate into $Y$ by using their respective inverse CDFs.
