To apply the right hand rule, first establish a a position vector $$\vec{r}$$ pointing from the rotation center to the point of application of the force, or another point on its line of action. If you align your thumb with the position vector and your index finger with the force vector, then your middle finger points the direction of the moment vector $$\vec{M}\text{.}$$ Alternately, you can align your index finger with the position vector and your middle finger with the force vector, and your thumb will point in the direction of the moment vector.
Another approach is the point-and-curl method. Start with your hand flat and fingertips pointing along the position vector $$\vec{r}$$ pointing from the center of rotation to a point on the force’s line of action. Adjust your hand so the force vector $$\vec{F}$$ pushes fingers into a curl. Your thumb then defines the direction of the moment $$\vec{M}\text{.}$$