How do I remake my floor using hardwood such that it will not squeak at all?
Use screws instead of nails to hold the plywood down.  If you can, screw it into the joists, not just the existing floor.  You can also put down some glue betwen the plywood &amp; subfloor to prevent the plywood from moving at all.  Use tongue-and-groove plywood if possible.

If that doesn't help (and you should be able to do that &amp; check to see if you still have squeaks before putting down the hardwood) you might need to beef up the joists, or add additional bracing, from underneath.  Not so hard if the ceiling below is open, a lot of work if it's finished.