All carpet is made up of rows (like a cornfield) If this section is on a wall, then this is what you do. Untuck the carpet from the baseboards around the area you will be working on. Put tape just one inch outside of the place you will be cutting. Take a knitting needle ( big thick one), or a pen (witch ever works best for you) and gently seperate the row with the needle. You will have to do this cross wise too, and this can be more time consumeing. Then with a cushon back cutter,slowly make the 2 cuts. And check to see if you stayed on the row.
Now take the new peice, and do the same thing. Run the rows with the needle, and cut the carpet on just that two sides.Then seal the seam. (seam sealer) Take some hot melt seam tape, and a seam iron ( both found at HD) and slowly heat up the glue and move the iron slowly down the carpet, closeing the seam as you go and putting something flat on it afterward. (that slides along with you.) and your done! Restreach the carpet, and trim the new peice so it fits the wall, and tuck in.