Remove the trim around the perimeter of the floor using a hammer and crowbar. Then remove the prefinished flooring using the hammer and crowbar. Hammer down any remaining nails. If the plywood underlayment isn't fully intact, pull it up and replace it before proceeding.
Cover the subfloor in paper underlayment, rolling it out in slightly overlapping rows and stapling it down.
Use your chalk snapline to lay a starting line along the side of the floor where you want to begin. Put the line 1/2 inch out from the wall.
Set the first oak floorboard on the starting line, so the grooved side is facing the wall and sitting 1/2 inch out from it. Use a floor nailer to drive nails through the surface, putting them every 10 to 12 inches along both edges of the board.
Set the second board off the end of the first, connecting them by their tongue-and-groove milling. Repeat, setting the boards one by one along the starting line, nailing each one down as you go. Use a miter saw to cut the final board of the row.
Lay the next row of boards alongside the first, locking them tightly at the edges. If you can't get them tightly set to each other by pushing on the boards, then set a piece of scrap wood against the board and tap it with your hammer. Angle the nails in through the sides of the boards (instead of down through the tops), about one per foot. Cut the last board as needed.
Repeat and continue, building across the floor row by row. As you go, arrange the boards so the ends are staggered between rows and not lining up. Cover the whole floor.
Use a table saw to cut the final row of boards lengthwise to fit along the ending side with a 1/2-inch gap remaining at the wall. The floor is now ready for sanding and finishing. Floor trim will hide the gaps later.