Easy PCB trace width calculation
Since it says current in A, it seems I should start at 1.0, go right, down, left, and get around 0.04 [inches].


Yes, basically just follow "Example #1".
But you said you have 1 oz copper instead of 1/2 oz copper, so that should put you at about 20 mils trace width.


  Is this completely independent of the voltage? 


Yes


  Should I take the voltage into consideration for calculating the trace clearing?


Yes, but at 5 V you won't have any particular clearance requirement. When your working voltage gets to 50 V, start worrying about clearancescreepage and personal safety.