How does your noontime shadow change throughout the year?

The specifics change depending on the latitude in question, but the noontime shadow will become shorter as the sun's direct rays of incidence approach the latitude in question and longer as the sun's direct rays of incidence recede from that latitude.

For example, if you live at 45 degrees North, your shortest shadow will be on the summer solstice, since the sun's direct rays of incidence are at 23.5 degrees North on that day and will be south of that position on all other days. Conversely, if you live at the equator, your shortest shadows will be on the vernal and autumnal equinoxes, since the sun is directly overhead on those days.