in a tape player the tiny magnetic differences in the tape cause tiny voltage changes in a coil inside the tape read head. these voltages come out the back (usually 4 pins, two left two right) and then get passed into an amplifier circuit that boosts the voltages high enough that they can move speaker cones. its a very simple system that is entirely analog.
if you wanted an Aux in, you could wire straight to the back of the read head or where the wires from the read head go to.
in those tape adapters they use a read head just like the one in the player with tiny coils in it. the low voltage audio from an MP3 player for example, causes the coils to become magnetic, which is passed to the read head in the tape player. this is similar to how a tape can be recorded by reversing how a tape player works.