I am just learning how to work with Corian countertops and I would like to know exactly what I should be doing since I don't have much room for error.

Corian Work Just Like Wood, Same Tools Are Used. If Your Making Joints Then A Skill Saw Can Be Used But You Need Clamps And A Straight Edge
As Far As Making Joints I Know They Use A Special Glue And Clamps To Bond The Edges, And I Don't Know What That Is Exactly.
If Your Not Doing That And Say You Have A Scrap Your Messing With Run In The Table Saw If Possible, You Can Also Route It With Regular Wood Carbide Bits. Good Luck

Glavine is correct that woodworking tools are used with Corian. However, carbide blades and cutters should always be used. Get training before trying any complex Corian fabrication. You can learn a lot on my website:

Top Repair - Your Countertops Like New Again. DuPont Corian and Other Brands (http://www.TopRepair.com)

- Jim Heaphy

I am just learning how to work with Corian countertops and I would like to know exactly what I should be doing since I don't have much room for error.
What is the best way to cut corian countertops?

Your question isn't specific enough, bobbybob23. The best way to cut a Corian countertop in a residential kitchen would be different from the best way to cut it in a small custom fabrication shop. And that would be different from the best way to cut it in a large automated production shop. Are you a do-it-yourselfer or a pro? Are you making a straight cut, or a cutout for a sink or a cooktop. Cooktop cutouts have very exacting requirements. Ask a more detailed question and you will get a much better answer.

I am a do-it-yourselfer, making a straight cut to just trim off the edge so the rnage will fit better.

I'm a plumber with 14 yrs exp. I need to cut a corian countertop to unstall a new cooktop .I have to cut1/2 in on one side & a1/4 in on the other .what 's the best tool

I've always made my rough cut with a table saw,with a carbide blade. I cut the my measurements to about a half inch over of what I need, because I will use a router to finish my edges. I use the scrap square edges for straight edges and guides for the router by using a hot glue gun to attach them. You can also use a jig saw, but always make a rough cut and finish with router