This task is done all the time and it can be done very professsionally with a few ket tips:
Terms, tounge is the wood that has a protrusion like your tonge sticking out. groove is the channel cut into the adjoining piece to accept the tonge, hence it has one groove, but two channels.
Identify the bad board and remove it any way possible but do not damage the outlying boards. Normally you can drive a chissle into the middel of the bad board and literally chip it out. But, again, do not damage the outlying boards.
The next part is pretty hard to put into words, but I will do my best; once you have removed the bad board and cleaned out the vacant area of all debris and nails and junk, and have made a nice new piece measured and dry fitted to act as a replacement.
Now, As you know, the tonge of the new piece wil fit into the groove of the board already in the floor, but the problem is that the groove of the new board will not go "down" into the vacant hole because of the grooves on the new board will not fit into the tonge of the board already in the floor. You will realize that the bottom groove of the new board does not allow the existing tonge to fit.
Here is where you have to carefully and dilligently remove the bottom groove of the new board so it will slide and fall into the vacant hole.
You can do this many ways, the best is to set your table saw for a setting that will only remove the groove bottom lip and leave the groove open to fit in. Setting the depth of the saw is the key.
Secondly, you can carefully with a sharp chissel tap and whittle off the bottom lip. Whatever method you use, take great care not to damage the groove or the upper lip of the new board. Do not think ahead and try to remove the tonge of the existing board in place, this will be needed for a good seal.
Keep whittling away and chisseling away until the new board fits nicely into the slot and when its to your satisfaction, apply daubles of glue to the adjoining boards for the new board. Apply some to the back of the new board if you want. Many will disagree with this as the floor needs to be able to move, but the original floor was nailed down anyway.
Now, with this in and cured, you will notice that the new board is slightly higher than the existing floor, sanding will be needed to make it smooth. I would save all the sawdust for later use in the finish touches.
When sanded down, blow out all the dust and clean the area well, do not allow water to get around the new board as it will swell up. Now, if you want, make some putty with the dust and glue to fill in any cracks around the new board and the butt joints. Let this dry and sand again. Always sand with the grain.
Now, stain the board and seal it. You should be set.