In an AM radio do the electromagnetic waves cause the antenna to resonate to produce an alternating current?
Looking at Hertz's original experiment with electromagnetic waves with the spark gap how did he know how to build his antenna size to receive the wave that generated the spark ?


First of all, the spark doesn't have a "single" frequency/wavelength. It's an extremely broadband emitter, so he could have chosen any length within a large range. 

Then, Hertz came after Maxwell - so, all the math was known to him (though he went through great efforts of making that math usable, and teachable to students, as he was the first generation of EE professors in the world, and taught EM theory, as well as half of the rest of the EE curriculum at the University of Karlsruhe). So, he's the one to describe the Hertzian Dipole as model for an "infinitesimal antenna element" – and thus was also able to model the antenna as an array of those, leading to a frequency selective antenna.


  In what way is the AM antenna like a spark gap receiver?


There's no such thing as an "AM antenna". AM is a modulation. Antennas are selective for carrier frequencies and signal bandwidths.

In any way, an antenna is just a conductor that gets excited by EM fields.


  So then any metal object will produce an AC current when an electromagnetic wave hits it?


"produce": no. have a current induced internally: yes, as long as the wave doesn't hit it perfectly in an angle that leads to the conductor extending only in a direction of constant E-field.


  And an antenna is constructed to resonate at some particular frequencies in order to amplify the signal?


"amplify": no. pick up the wave's energy at that frequency: yes.


  Basically I am trying to understand what makes an antenna an antenna so to speak.


Antenna Theory – it's a large field, and you should probably start reading a textbook. Probably, amateur radio clubs do have beginner-friendly intros to antennas.