How does the position of the sun in the sky affect the intensity of sunlight striking earth's surface?

First, the surface that the sun faces is almost always the same, but it changes the "position" during the lapse of a day.

Now, if we have a fixed position, as the day phases the effective area that the sun "sees" changes.

For example at the beginning of the day, the sun only sees an ellipse, when the sun is right above the area, the sun sees a surface like a circle, and as the sun starts to go away the surface turns again into an ellipse.

you can see this as holding a ball with a region painted on it and start to rotate the ball, you will see that in some positions you will not see the painted region, and as you rotate it you will start seeing a little part, then the whole part, then a little part again, and so on, where in this case your vision represents the sunlight, and the painted region is the fixed area of the planet.