From a friend born and raised (and still living in Quebec):

Pou like in Winnie the POOH (short) and tine like in a TIN can.
A WAV of the proper pronunciation of "poutine": POUTINE.WAV

Some further miscellany:

At this site they say poutine comes from Gaspesie.... WRONG!!!! Everybody knows it comes from Warwick (little town near Drummondville) Ben voyon donc!! Also a Historical pountine site I didn't look at it closely. BEWARE of the recipies that you could find on this site. (you will have to practice you french

http://www.geocities.com/NapaValley/2111/Historique_de_la_poutine.html

I can not emphasise enough, Beware of these recipies. You should know that a good poutine is made with home made fries, with fresh cheese curds (it makes this squish! squish! sound when you shew them) and universal hot chicken sauce (St Hubert sauce in can is the best - Hope you have some in your area). Now, A very important step is the way to distribute the cheese in the fries. I personnally like to start eating a few fries soaked in sauce before going for the cheese (A question of equilibrating your salt concentration on your tongue!!) So I would dispose in a bowl or if you really really want the real thing in a styrofoam or alluminium bowl (disposable of course) a few fries then some cheese then a mix of fries and cheese and finish with a layer of fries. Of course you could sprinkle a few curds on top (for the french cuisine look! HA!) then soak this in universal sauce. But remember start with the fries.

All of this if of course of personnal taste and can be modified ad libidum!!