Welcome to the site mate
I've replaced 6 Mk3 fiesta sills now so yea, what I did was cut the old sills off with a cutting disc on an angle grinder. Underneath I cut it just back from the flange and on the top I leave about 15-20mm of the original sill underneath to give me something to weld to at the top.
You can buy two types of replacement sill, full sills and skin sills. The full sill includes the doorstep aswell but I use skin sills as they are easier to fit and the doorsteps on my cars were fine. Also, using skin sills means you don't have to do any bodywork or fillering afterwards.
When you get the skin sill, you need to measure and cut a little bit off the top in order to fit it without it sticking out of the bodykit and being visible when done. This includes the bit where the rear quarter panel is because when you buy the sill, it comes with a bit extra to join up to that panel by about 10mm but this would need blending, filling, smoothing and spraying so just cut it off like I have as you can see in that pic. This means no work is required at all on the rear quarter panel.
On the bottom flange, once you've cut the sill off as described above, remove the rest of it by cutting upwards on the bottom flange to remove the front layer which is the sill. the flange is made up of three layers, the sill, the inner sill, and the floorpan. Just remove the sill layer (this will all be more obvious when your doing it, trust me lol)
Next, clean up the bottom flange to shiney metal and also the top flange ready for welding. Drill holes in the new sill ready for the spot welds then clamp it and weld it on, grind the welds down and paint it, jobs done
My car needed some patches to the inner sill as the bottom flange had literally rotted away so I had to do this first so I had something to weld my new sills to. Yours may need this too, but if you find it does or come accross any other problems along the way, just drop me a pm and I'll be happy to help