To apply the right hand rule, first establish 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 right 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. Rotate your hand until the force $$\vec{F}$$ is perpendicular to your fingers and imagine that it pushes your fingers into a curl around your thumb. In this position, your thumb defines the axis of rotation, and points in the direction of the moment $$\vec{M}\text{.}$$
Consider the page shown below on a horizontal surface. Using these techniques, we see that a counter-clockwise moment vector points up, or out of the page, while the clockwise moment points down or in to the page. In other words, the counter-clockwise moment acts in the positive $$z$$ direction and the clockwise moment acts in the $$-z$$ direction.