The ideal solution is to replace the damaged plank. There is a method for this (see below). It would be useful if you have a spare plank still available from the original laying process. The next best option is to buy a matching replacement plank (you'll have to buy a pack, though). If you cannot get hold of a matching replacement, and you really, really, want a proper repair, the job will become a lot more difficult, because you will have to rob one from a hidden or less conspicuous part of the floor. I won't go into that process unless you ask for the information.
So, assuming that you have a perfect and spare plank available:
You need a circular saw and some confidence. Set the depth of the saw to 1mm less than the depth of the laminate. If you don't know what it is, set 6mm, which is 1mm less than the thinnest laminate I know of. Using the saw, cut out an inset rectangle just inside the edges of the damaged plank. If you are unsure how to start the cut, practice lowering the saw by cutting a few grooves in the middle of the plank. Once you are ready for the actual job, cut as close as you can with confidence such that you will not cut a surrounding plank. Then, using a chisel, gently push though the remaining laminate at the bottom of the saw cut to expose the underlayment, trying not to damage it. The inset rectangle can now be removed, leaving a rectangular frame. Then, using a sharp chisel, cut one short side of the frame at both ends away from the 2 adjacent long sides. Without damaging the tongue (or groove) of the adjacent plank, carefully remove the short side by pulling it out along the floor. Do not pull it up at angle, because the tongue or groove of the adjoining plank might become misaligned and you will end up with a slight bump in the floor when the job is eventually completed. Now make a similar cut on one of the long sides, at the other end of the chosen side, and remove it. Then do the same process for the remaining 2 sides.
You will then be left with a floor without the damaged plank, and all the adjoining planks will be in a perfect condition. If the original damage affected more than one plank, you will have to do the same procedure for all affected planks.
You will see that there are tongues on 2 adjacent sides and grooves on the opposite sides. You will not be able to fit the new plank using all the tongues and grooves. On the long side with the groove on the new plank, you have to remove the lower (underside) of the 2 tongues that combine to produce the groove. This will allow the top tongue to sit on the tongue of the adjacent plank. Then do the same on the short edge lower tongue.
Ensure that the gap is thoroughly swept and hoovered to remove all bits of dirt and dust, etc.
Apply copious amounts of strong adhesive to the tongues of the planks on the floor and the underside of the top tongue where the groove used to be on the new plank. Slide the new plank diagonally into position such that its tongues fit into the grooves of the adjoining planks. The top half of the new plank's grooves should eventually sit neatly on the tongues of the adjoining planks. Wipe away excess adhesive and place a heavy object on the new plank while the adhesive cures.
Thats the best advice I can offer. WoodYouLike is the expert here and he might offer better advice.
Best of luck
