With so many different website claiming to have cheap flights and cheap hotels, how can you be certain that there isn't some other website offering the same cheap flights at an even cheaper price? Apart from searching every single travel website on the web (which run into the millions!) you will need a great search comparison box, or two or three search comparison boxes that search through all of the web's best sites for cheap flights. You should also remember to be flexible with your dates if possible as the price of flights can vary drastically from one day to the next.
Another thing to consider is looking at two one way flights, even on different airlines that you know fly to your destination. You can usually get this information by going onto the city's airport website. You should also search nearby airports if the cost of the transfer into the city is not too much. You can usually save a lot of money by searching for flights this way.
Check when the school holidays are at your departure airport as well as your destination - airlines push up their prices during school holidays so you can save a lot of money by looking for flights at the time of year when schools are in! It is also worth checking religious festivals in your country and the country you are travelling to as the there will be no cheap flights to be found anywhere! An example is Christmas time and New Year for Christians which is in late December / early January when flights are very expensive, unless booked in advance. You should always remember to book your flights as far in advance as possible anyway as you will usually find they are much cheaper that way.