I was wondering how one could make a simple volume control for a 555-speaker circuit, by like using a potentiometer?

 

What your doing will work, but I think this is a better approach...

For one thing the volume will actually go to zero.

 

Thanks a lot! I am curious, what does the capacitor do in this circuit?

 

Decouples the DC from the speaker. You don't really want steady (possibly high) current going through the speaker, all you're after is the AC component. Think 220µF or more.