The way the collar works is there is a small sound impact sensor on the inside that listens for your dog's bark as it comes from his throat. That triggers the Arduino to read a potentiometer that tells it which type of voice to choose. Then the last step is the Arduino chooses which phrase to say and plays it over a speaker in the collar. To do that, we need a few parts.
Main Collar Parts List
Arduino (I use a Duemilanove... $25-$35 depending on where you buy it. The Uno is the latest and greatest, but I bought my Arduino a while back so it isn't the newest one http://www.spikenzielabs.com/Catalog/index.php?main_page=product_info&cPath=12&products_id=40
Adafruit Wave shield (I went with a Music and Sound Pack just to be sure I would get an SD card that worked properly and it came with a speaker)
Wave shield $22 (If you choose this option you will need to buy an 2GB max SD card and a small speaker that is still loud enough to work at normal room sound levels) http://www.adafruit.com/products/94&zenid=80d8423d846699d9ee654a2b86118553
Music and Sound Pack $35 http://www.adafruit.com/products/175&zenid=80d8423d846699d9ee654a2b86118553
Shield Stacking Headers (at least one set) $1.50 http://www.adafruit.com/products/85
Adafruit Proto shield $12.50 http://www.adafruit.com/products/51
1/4 size breadboard (for Proto shield) $4 http://www.adafruit.com/products/65
Sound Impact Sensor $7.99 http://www.parallax.com/Store/Sensors/PressureFlexRPM/tabid/177/CategoryID/52/List/0/SortField/0/Level/a/ProductID/614/Default.aspx
10-inch Extension Cable with 3-Pin Header $2.25 http://www.parallax.com/StoreSearchResults/tabid/768/List/0/SortField/4/ProductID/385/Default.aspx?txtSearch=3+wire
9v battery holder $4 http://www.adafruit.com/products/67
10K-Ohm linear potentiometer A local electronics store should sell these for 3 or 4 bucks
Fancy "Control Knob" for potentiometer These will usually come in a four pack and run about 3 dollars. Pick whatever you think looks the best, but make sure it will fit the shaft size of the potentiometer you bought
1/2 a yard of Pleather $5.99 (I ended up using about half of it, but get extra in case you make a mistake. Everything's 65% easier the second time around!)
Thrift Store belt with a large metal buckle $1 (Only want the buckle... mine is just under 3 inches wide)
Spool of Coats Upholstery Thread $2.20
Two pouch fasteners (I used self adhesive velcro squares, but if you're better with a sewing machine you might try buttons)
Misc Parts List
Rosin core Solder
Assuming you have the tools but need to buy the collar specific materials, this project will cost you just over $100 USD. Not too shabby to be the only owner of a talking dog on your block!
There is only one Sketch for this project so I will link in at the bottom of Step #4 (When the shields are assembled to the Arduino but before they are put inside the Talking Collar).