To determine the intersection point between a ray and a 3D polygon, specifically a triangle, the equations of the plane and the ray must be established. The plane can be represented by the equation Ax + By + Cz = d, while the ray is defined by parametric equations. By substituting the ray's equations into the plane's equation, one can solve for the parameter t. If t is greater than or equal to zero, the intersection point can be calculated; if t is less than zero, the ray does not intersect the plane. Additionally, checking if the intersection point lies within the triangle can be done using barycentric coordinates or other geometric methods.