All the tour books say that this is a must-try spot in Montreal and while sometimes that is a sign to actually stay away because it is overhyped or touisty, I definitely recommend that you try Schwartz's! In fact, I thought the corned beef, which has an extra layer of smokiness to it (compared to regular steamed/boiled corned beef), was better than stuff I had in New York! (I can hear gasps and cries of how unAmerican I am now)
When you go, do:
-be prepared to wait in line outside for 15-30 minutes and expect to be seated at a table with strangers. It's all good though
-order the regular, not lean. You ain't eating here because you're watching your calories.
-pass the mustard or ketchup or whatever your stranger-dining-mates on the other side of the table ask for.
Despite how small the dining room is and how crammed it is with people, it is fairly quiet inside. And after you take your first bite you too will shut up and understand why. :)