How to do it

carefully

Do a search on Youtube for several videos.

Many use a router for edges and a plunge router for cutouts, if I remember back 30 years.

Depends on what you are attempting. Cutting a whole panel? Enlarging a sink cut out? Putting in a hole for something else? Corian is a plastic material and very dirty to cut. Check out the above mentioned videos.

Hello

Ok , for the love of god don't use anything that is dull , blunt , not sharp etc.

With that out of the way.

Routers .

Use a heavy duty router with a straight bit and a fence. Again, cut in several passes for the safest, cleanest cut.

Belt Sander.

For small cuts, you may find a belt sander with a 50-grit sandpaper will work down 1/8 to ½ inches fairly quickly and with more accuracy than cutting. This is a particularly useful technique if you have uneven walls that you must accommodate.

Hope this helps.