Left adjoint to forgetful functor between varieties of algebras

Question

Given algebraic theories $S$ and $T$ for which there is a forgetful functor $U : S_{mod} \to T_{mod}$ (e.g. $U : \textbf{Rng} \to \textbf{Ab}$), it is known that $U$ is monadic, and hence has a left adjoint $F : T_{mod} \to S_{mod}$. Is it known how to compute this left adjoint in general? I.e. given a $T$-model M, is it known how to compute the $S$-model $F$(M) in general?