Magnetite is a common iron ore. This ferromagnetic mineral has the chemical formula Fe3O4. Use a strong magnet covered in paper to sift through sand or dry clay powder. A significant number of magnetite particles should be sticking to the paper over your magnet. Place the particles in concentrated hydrochloric acid. They will dissolve to form a yellow solution. Add sodium bicarbonate (baking soda until a precipitate just begins forming, then add one drop of hydrochloric acid to dissolve the precipitate. This slightly acidic solution of iron(II) and (III) chlorides can then be reduced with zinc, magnesium, or electrolysis to produce a magnetic precipitate of iron metal.
Of course, this complete process has no industry uses because 1) zinc or magnesium is much more expensive to extract than iron 2) zinc is much rarer than iron 3) wet chemistry is not as easy to perform as dry chemistry 4) iron rapidly corrodes in wet environment. However, pure iron is produced by electrolysis of an aqueous solution of an iron salt.
Taking this a step further in the engineering direction will involve obtaining coke and limestone and producing a miniature blast furnace.
Taking this experiment a step in the interesting direction will involve obtaining fine aluminium powder, grinding it in a mortar and pestle with the magnetite particles, and igniting with magnesium ribbon in a crucible (thermite reaction, research before reacting)