How can I repair/replace a water damaged plank in my floor?

If you laminate floor is a "click together" floor (one that doesn't use adhesive to bind planks together) you're in luck but it will be a slight paint to do. You'll have to start at one side of the room and remove planks until you get to the damaged one, replace it, and then reassemble. You might have to remove a piece of trim in order to get the first few planks out, but once you get going it should be easy.

Zacs answer is good, takes some time I suggest numbering the pieces you take up so you can put it back together the same way it came apart. However, if it is not click type or has been glued down it is still possible but not easy. Two approaches, if you have a couple of scraps of the flooring scuff up a piece, play around with some fillers/ glue /finishes/ etc, and try to replicate the finish. If you get it, try to refinish the damaged piece in the floor.

The second method also works but takes some care. First do you have a piece of the flooring large enough to replace the board. If not see if you can get one.

Get yourself a good utility knife and a pack of new blades. Carefully insert the blade into the joint between boards, with some down pressure you are going to score on all four sides. You will be cutting the composite material. It will take many passes increasing the depth of the score each time. ( you will have to change blades a few times ) At some point in time you will feel a change that indicates you have cut through a layer, either a tongue or part of a groove, that is good, but you are not done. Compare using a new board how far you have cut through. When you are convinced you have cut all the way through you should be able to, with some work, remove the bad/damaged piece. Cut your replacement board to length and check the fit and height. Shim for height if necessary and use adhesive to fix it in final position. It is critical to work slowly, take you time so as not to damage adjoining planks. Good luck hope this helps.

This is how I do it.

https://homeguides.sfgate.com/replace-laminate-floor-board-middle-floor-37327.html

https://www.youtube.com/watch?v=HeO4czmZ7kY

Good answer good advice, watch this.