Limited Surface Damage
If the water damage is only on a small section of the floor in an inconspicuous area, such as under a window or in a corner of the room, you may be able to repair just that section and blend in the new finish to match the existing floor. Let the floor dry before attempting the repair, and then sand off the wood finish over the damaged spot.
If the sanding removes some of the wood stain, apply a new wood stain to the spot to match the existing floor color. Then, use a fine natural-bristled brush to apply two or more coats of wood finish to the re-stained area, feathering out the edges of the wood finish to make the patch less noticeable.
Replacing a Few Boards
Constant exposure to water for long periods of time can make oak swell, warping some of the floor planks. If the damage is limited to a few planks in an inconspicuous area, you can remove the damaged oak boards, and take one into your local lumberyard to purchase replacement oak planks of the same width and thickness.
Cut and install the new oak planks, stain the wood to match the existing floor, and brush on new wood finish, feathering it out over the existing boards.
Refinishing the Whole Floor
Widespread damage to the oak floor's surface may require complete floor refinishing. Remove the old wood finish with a walk-behind random orbital sander, available from construction rental stores.
Replace any damaged boards, apply wood stain to the entire floor, and add two or more coats of durable wood finish.
If the oak flooring is damaged to such an extent that the individual boards are cupping, coming away from the floor joists at the ends and at the edges, the floor is probably beyond repair. In this case, the only option is to remove the old oak and replace it with new flooring.