I bought a badger 500 and I a, not using a dishwasher how do I plug the dishwasher connection

You plugged it into the wrong socket under the sink.

Dishwasher drain hose come in different sizes AFAIK.
You will need to get the right diameter hose to connect to the disposal unit or use an adapter kit. Search for InSinkErator DWC-00 Dishwasher Connector Kit about $7 from Amazon.

The manual is not informative on specs: http://images.insinkerator.com/pdf/badger500_icu.pdf

No you punch out the plug inside the fitting where the dishwasher hose goes.
Here is a link to the instructions look at step 15 and 16

Hope this answers all your questions
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You are missing that the plug needs to be removed on a new disposer. All new units have this port sealed as not every install will have a diswasher...Take the unit out, and look in the hole, woopsies. Push it out with a screwdriver and a hammer. this blockage would cause the water to come out of the vacuum break on the counter.
Fortunately not a big problem to repair.

There is often a plug in the ISE as many people use them without have a dishwasher connected to them. Quite often it is just a thin plastic membrane that can be knocked out with a screwdriver. There should also be a note to this effect in your installation instructions for the ISE.

It's not guaranteed that your particular model will have a dishwasher drain nipple, but it does, it'll be on the side, near the top of the machine. If the disposer is new you must knock out the plug inside the nipple before connecting a dishwasher. If the disposer doesn't have a nipple, you can get a piece of pipe to fit to the non-disposer side of the sink where you can connect the dishwasher drain hose.

Are you talking about the "barbed attachment" on the disposal? If so, simply use a screwdriver and hammer to knock it out. Make sure you reach into the disposal (through the sink) to get this piece of plastic out after. Good luck

if this was just put in it is most likely the packing plug was not removed when installed please take hose off and remove plug .

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Your inlet hole has to be opened up. Use a screw driver to tap the plastic plug and it will open. good luck.

From the dishwasher hose end of the nipple, insert a large flathead screwdriver or nutdriver and tap it with a hammer. They sometimes take a moderatly strong hit. It is litterally nothing but a plastic plug.

You will want to do this with the disposal uninstalled and the power disconected.

(doing it installed can potentially cause leaks.)

Make sure that you remove the little plastic plug that was knocked out from the inside of the disposal.