Let $M$ be a smooth manifold on which acts the $G$-action $\Phi$. According to the quotient manifold theorem, if $\Phi$ is free and proper, then the orbit space $M/G$ has a unique smooth manifold structure such that the projection map $\pi:M\mapsto M/G=\bar M:m\mapsto G.m$ is a smooth submersion and defines a principal fiber bundle with structure group $G$. A fiber of $\pi$ is a $G$-orbit in $M$ and is then diffeomorphic to the structure group $G$ with diffeomorphism $G.m\mapsto G:\Phi( g,m)\mapsto g$.
I would like to know if they are necessary or sufficient conditions on the action $\Phi$ that ensures that the principal fiber bundle is trivial. Thanks for any suggestions or references.