I see from your profile that you're located in France. So let's start with the possibly-obvious: Montreal is not in America, while Atlanta is. I mention this because train and bus travel across the US-Canada border is not exactly co-ordinated. Luckily many American bus and train companies offer service to Montreal. Some Canadian ones offer service to New York, but no further.
Second, the distance between these two cities is about 2000km. If you could drive at 100 km/hr without having to stop to sleep or eat, it would take you 20 hours. On a bus, which will make more frequent stops, it would take longer. And if you have to change buses in some intermediate city like New York, it will likely take longer still. This will apply to the train also.
VIA Rail implies on their website that they will take you from Montreal to New York, but you just end up on a web page that says to talk to Amtrak. On the Amtrak site I learned it is 11 hours Montreal to New York, and 18 hours New York to Atlanta, plus of course whatever the connectiin time is between the two. For the particular date I checked, the first train gets in at 8:20pm and the next one leaves at 2:15pm the next day, so you'd need to spend the night in New York. Sitting in a seat the whole way (the cheapest option) would cost you about $200.
In contrast, Air Canada will get you there with one connection in as little as 5 hours, for a price of $331 taxes and all. Unless your New York hotel room costs less than $130 a night, you will spend less money flying. You might find a better price on a low cost carrier - I just looked on the site I know how to use.
There are a number of cheap bus lines from Montreal to New York. I checked Greyhound.com and their lowest price is $89 and the fastest time seems to be 29 hours total - which is definitely both cheaper and faster than the train.
You still have more research to do - I didn't check all the airlines or all the bus lines, but this gives you the rough parameters. If spending between 24 and 48 hours getting there is ok for you, look further into buses. If you don't mind $331 but were worried the plane would be thousands, look further into planes. You can do most of this yourself over the web once you learn the names of the companies that offer the service.