Remove coverings such as carpets to expose the bare flooring. If completely removing the carpet in not a viable option, lift it around the edges of the room as far as possible.
Examine the floor surface for clues left by the builder. Sometimes the routes of ducts and pipes are marked on the flooring, either to help locate them or as vestiges of the builder's on-the-job planning. Clues include the obvious such as "duct" written on the floor adjacent to a wall vent and the not-so-obvious such as floor boarding aligning with two vents, suggesting that the duct may run directly from one vent to another.
Search for flooring boards that are shorter than others, boards held down with screws while those around are attached by nails and signs of damage around the edges of a board that may indicate that it has been lifted in the past. You also may find an "access trapdoor" built into the floor.
Scan the floor with a pipe and cable detector. Mark on the floor the locations of all strong responses. Ignore short "beeps" and seek out the strongest signals that indicate larger metal objects such as galvanized or foil-coated ducting. Examine the pattern of responses and, from that and the other clues, decide on the most likely location of the duct.
Select a floorboard as close as possible to the suspected duct location. Lift it to see what is there. Unscrew boards that are screwed down. Lift nailed boards by slipping a bolster chisel into the end of the board, hammering it in and then prying the board out of position.
Lower a small mirror and a flashlight into the cavity below the floor if you do not locate the duct immediately. Switch on the flashlight and point it along the floor cavity. Hold the mirror at 45 degrees so you can see under the boards to either side of you. Move the flashlight and mirror around to scan for signs of the duct.
Reassess the evidence if you are unsuccessful in Step 6. Lift the next most likely board. Continue lifting boards until you locate the duct.