Booking is now easier then ever and with many search engines to choose from you will likely find yourself a cheap flight to or from Heathrow airport. Simply put in the dates you wish to travel and the destination and the search engine will help you find the best price.
If you want the best price to a destination and you are flexible with the dates you can travel then you can use the same search engine to find the different prices for the month. You will then be able to choose the best price for that route.
If you find a good price then don’t wait too long to buy it. Prices go up as seats are filled and they very rarely go back down. Book your flight to or from Heathrow as early as possible and you will likely find a cheap flight.