Apart from your flight, you will probably spend the most of your money on accommodation. Especially if you are traveling on a budget (which to be fair, most backpackers are), you can find relatively cheap hostels on the following websites:
Hostelworld is my go-to hostel booking site. You type in your destination and your travel dates, and it will show you all of the available hostels. The website works worldwide. After you have typed in your destination, you can narrow down your search by selecting the distance from the city centre, the maximum price it can cost, and more. The website is very reliable and there are no hidden costs.
Hostelbookers basically works like Hostelworld. Here too you search for hostels by destination, but you can also apply a variety of filters.
Booking.com is used for all kinds of accommodation and not only hostels, which is why often times, the hostels you can find on Hostelworld or Hostelsbookers are either not on booking.com or are a little more expensive there. Nonetheless, if you are looking for a bed & breakfast or something a little more expensive, this is the website to go to.