What to use please? It's a lumpy lump of stone with tatty paint on at the minute.
I'd assume like most window sills it's got 100 years of paint on it
With a paint scraper scape off all the loose paint.
Then using a sander with fairly course sandpaper rub down the rest, you are trying to give it a smoothish surface
Then using something like polyfiller (not flexible one, the hard one) fill all the divots and ensure the places where the paint has come off down to the stone are filled and given smooth edges
If there are major chips put of the sill edges these can be filled with polyfiller as well.
The professionals often use offcuts of (very expensive) Amtico lino flooring to give a sill a perfect edge and then fill all the lines so that it looks perfect
Then paint. It will be several coats of a good quality exterior masonry paint.
The perfect time to do this job is mid summer, but hey ho.