Hello. I have to remove screws that are totally stripped from an exterior storm door to replace the door. What is the best way, and tools, to go about doing this?

Thank you.

Pick up a damaged/stripped screw remover kit from a local hardware store. They're fairly common:
damaged OR stripped screw remover -

Are these the wood screws on the exterior of the frame and by "stripped" do you mean that the heads are mucked up? If so these are aluminum and are very soft? That's why the heads are mucked up. Cut the heads of with a hammer and a small wood chisel.

If the chisel will not do it try to drill the head off. Start with a small bit to keep the hole centered. You could even pull it with a cats-paw. A grinder will also take the head off and flush up the remainder.
Happy door hanging.
Helmer

Cut a slot with a Dremel tool.

Tha dremel will be a frustration if the screws are indeed the aluminum round heads stroud mentioned. Those do chisel off very easy.

Probably true.

Removing stripped screws is always a frustration.

I had one interesting removal problem. I had nylon thumbscrews holding in the screen and/or glass in a storm door and the heads of a few were removed. I used one of the "dental-like cutters" to put a small slot in about 10-24 stud. It then removed with a small screwdriver.

Very nice. That procedure requires great skill!

I'm totally ambedexterous. I can write script left hand, right hand, forward and mirror image.
I use what hand is convenient

Thanks for the complement.

1/4" diameter hole cutters work well when the heads are sheared off and you wand to replace the screw in the same hole.