Susan,
That looks like the same switch that I have in my router/shaper and drill press, so my initial posts seem to hold true. It's a 2 pole switch and Ace hardware might have an exact replacement for it, so it's worth looking there. If you find one, don't throw your old switch away. After cleaning, it will make a good spare.
The removal and cleaning process -
At the top and bottom of the switch (when positioned like in the picture) there are some plastic fingers that need to be pressed in toward the switch body while you press and wiggle the switch forward from the back side to push it out of the panel. You may need to get the fingers on one end of the switch to release and then get that end of the switch pushed slightly forward before doing the same with the other end, to get it completely out of the panel.
Cleaning -
Then you should be able to see the seam between the front and back half of the switch body and little plastic latching clips on the narrow sides of the switch (top and bottom) that hold the switch halves together. When these are released you can pull the front and back halves of the switch apart and clean out the sawdust. Be careful not to loose the rocker contact assembly and spring that are loose inside the switch.
Once the sawdust is out, you will need to put the rocker contact and spring back into place before putting the front and back halves of the case back together. Do this with the switch handle pointing up and the back half of the switch sitting on it's contacts on the workbench. When you get it back together, Turn it on and off to see if it operates correctly, then put it back into the saw and re-connect the wires. The wires from the motor should go to the bottom terminals and the wires from the power cord should go to the upper terminals, one color on the left and the other on the right. Both white need to be on one side and both black on the other, but it doesn't matter which side is which. Now wrap some electrical tape around the body of the switch to seal the holes and seam in the switch body as best as you can. Doing this should give you more use before it needs to be cleaned again. It's not likely that your seal will be perfect so eventually this will happen again. Delta should have chosen a sealed switch design for these tools. Your saw should now be ready to use again.
If this doesn't work for you, send me a PM. I've got some other ideas that I think will solve your problem, if cleaning your switch out doesn't work.
Don't spray any cleaner liquids into the switch.
Charley
I just checked ToolPartsDirect and their website says that they have 3 switches in stock for your saw, but EReplacementparts.com doesn't show that any are available.
I normally by from EReplacementParts.com, but have purchased from their competitor in times like this. I've never had any problems with either company.