Buckled boards on your hardwood floor mean moisture has gotten in there and expanded the wood, forcing those boards up and out of their fittings with the surrounding boards. You should first try just nailing them down, but that often won't work, since the boards are probably permanently warped. Usually, they'll have to come out, which is a delicate operation, since you have to get them out and replace them without ripping apart the tongue-and-groove milling on the surrounding boards. (Obviously, you need to identify and address the moisture problem first.)
Things You'll Need
Small, sharp chisel
Replacement tongue-and-groove floorboards (same kind as the existing floor)
Put masking tape along the outer edges of all the boards that need to be replaced, bordering off your work area so there's no confusion once you get started.
Set your circular saw to the exact depth of your floorboards (use one of your replacement boards as a guide). Run the circular saw along the middles of the damaged floorboards lengthwise, cutting in parallel lines. Don't let the blade hit the edges of the bordering parts of the floor.
Use your hammer and chisel to dig out the cut-up scraps of wood from the middle of the boards, so you're just left with bordering areas of each board connected to the surrounding floor with tongue-and-groove milling. Use the chisel to gently pry the last pieces of the damaged flooring away from the surrounding flooring.
Measure and cut your replacement boards to size on your miter saw. Lay a bead of carpenter's glue along the tongue side of each one. Starting on the side of the exposed floor where there is an open groove (instead of a tongue), begin pressing the new boards into place, locking the tongues of the new boards into the grooves that are there. Do all but the final course, where the tongue of the existing floor is exposed.
Lay your last course of new floorboards face-down on a work surface. Use your razor knife to cut away the bottom lip of the groove (now positioned on top), so you will be able to press the board into place over the tongue portions of the neighboring floorboards. Put glue on both edges of the new boards and set them into place.
Use your nail gun to nail all the new floorboards down, putting pairs of nails about every foot.
Wear eye protection when cutting out the old floorboards.