DON'T try to look into a running dishwasher! You can't see the leak this way, and you'll get a bath besides!
If you remove the foot panel at the bottom front of the machine, you can look underneath with a flashlight while it's running and see where the leak is coming from. There are two major seals around the motor- the shaft seal and the tub seal. The tub seal will drip down around the motor (but not down the shaft) whenever the tub is filled; the shaft seal will leak down onto the slinger( a round plastic disk on the motor shaft which will 'sling' water off its edges when the pump runs)
Other places to check are the drain hose and the fill valve & supply hose. All of these can be fixed with the washer in its installed position- you don't have to pull it out from under the counter. Before you put your hands in under the washer, be sure the electric supply is disconnected; all wet and live current don't mix well! There's a good d.i.y. repair manual available at repairclinic.com that describes all of this.
Phil, October 2005