The general principle is you cut the length of the board with a circular saw set to a very shallow depth, making sure to not over-run in to adjacent boards. Then you use a chisel or utility knife to cut all the way to the end. You should then be able to lift the middle of the board out. If the ends are also T&G, you might need to use a utility knife to cut the tongues.
Now for the new board: Cut the tongue off the short end. Then cut the bottom of the groove off from the opposite short end and the long side. Apply glue to the tongue and the (modified) groove. Slide the board in to place by inserting the tongued edge in to the appropriate board in the floor and rotating the board down so the (modified) groove edge fits in to place. Apply liberal pressure to the long edge, wiping up excess glue with rag wetted with warm water.