Don't pee there! Device
You probably will want a moisture sensor like this one (there are many variations of this).

This will return one signal when dry, and another when wet.

You will need a Buzzer to make a sound as well (Or a piezo speaker if you feel like getting more advanced) in order to make a sound.

Your sketch should have, in its loop, an if statement checking if the moisture sensor has returned the wet signal (The signal will depend on the sensor you get) and, in the block that executes if there is a signal, a statement driving the buzzer and a delay before turning it off.

Bear in mind that you want to keep the Arduino itself away from the moisture sensor, as your Arduino probably won't survive the dog's doings.