From where?
As you don't say, then all I can suggest is that you look around on air fare comparison sites such as Kayak to see what's cheapest from where YOU are. Avoid holiday periods and any time school is out - it'll cost more then because that's when families want to travel.
From the U.S.?? American Airlines/U.S. Airways are usually slightly cheaper than the others but for a little more money
British Airways, Delta and Virgin Atlantic offer better punctuality and service
From Canada Air Transat are generally the cheapest
It rather depends where you're coming from, when you want to travel, and how far in advance you can book.
Take a look on comparison sites like SkyScanner or Kayak to see what kind of prices you can expect.
From where? It may be obvious to you, but not to the rest of us!
Go on sites like Kayak, where you can search across different dates, routes and carriers, to find the best deal. Avoid the peak travel times, such as Christmas / New Year, Easter, and summer holiday (July/August especially).
in the Off Season- like January- February
Summer/ Spring Break/ Christmas are the Busy travel times and when Prices are at their Highest
By air
From where?