Most window sills can be removed with a pry bar and re inserted fairly easily.
You do want to be very careful in doing this as not to spring the window casing and breaking the glass. Any binding on the casing will make for a hard to move window.
Once you get the window sill out, preferrably in one piece, you can make a template out of the old piece. This is the ideal situation, but not always possible. Most of the time I have to free hand the new sill.
When you do this job, I always go back with Pressure Treated Wood so that I won't have to do this window again.
Once the new sill is cut, insert it and allow for an angle so the water will run off the sill. Flat sills are not acceptable!!!!!!! Then caulk with a good paintable silicon caulk and screw down the sill, no nails.
Then prime the PT wood after it has dried out good, then hit your finish coat and walla, you are set.
Now, many sills are different and procedures may vary with your window, but they can be eyeballed and the procedures made accordingly.