I once had the extreme displeasure of witnessing a shopmate sever fingers from his hand on a tablesaw. We wrapped him up and immediately took him to the emergency room. I was told later that the proper procedure would have been to call the EMTs and wait. It's a gruesome subject but it's prudent to prepare for the unexpected. I would be grateful for any ideas or comments.
A useful thing to keep in your first-aid kit is ice packages. They come in a format that all you have to do is smash them to activate the ice. This ice will keep dismembered fingers in better shape for later reattachment.
Do not put the severed part in water. The ice pack mentioned will do quite nicely to keep the part cool, not shriveled like a prune. Of course safety and respect for these machines is always the best way to avoid such occurrences.
First and foremost, you never place severed body parts directly on ice. The exposed tissue will suffer almost instant death when in contact with the ice. Ice is O.K., but you need to wrap the fingers (for instance) in gauze or a clean cloth, then place them on top of the ice.
The blood vessels in your fingers are pretty small. Bleeding can easly be controlled with direct pressure. As far as shock, this isn't an issue. IVs in these cases are used more for the administration of pain medications than fluid introduction. Besides, IV fluids don't have the ability to carry oxygen. Only your own blood does (actually red blood cells).
Injuries to great vessels will be quite bloody, but you can control even this type of bleeding with direct pressure. Tourniquets are a no-no. They cut off all blood supply beyond the tourniquet. You stop the bleeding alright, but the extremity dies. The most important thing you can do is keep the victim calm! Excitement will breed excitement. Calmness will breed calmness.
I'm an avid woodworker myself. Being safe is job 1.