Cheap is a relative term, a lot of practical and better advice have already been given however, there are a few watch outs in my opinion, which can leave both positive or negative impact on one's budget.
Season: Travelling at the close or far end of the season can give you better rates overall. This will vary from place to place and country to country. For example, Summers are the season for northern Pakistan, but same summers are off season in Thailand.
Accommodation: location of accommodation is most important as it will save you money in walking to some major attractions rather than save money and pay for taxis. Nowadays, Airbnb and couch surfing are options that weren't available earlier. Some hotels have chains around different destinations and they may offer deals like stay 4, pay for 3 nights, explore the option.
Food: Booking a hotel room without breakfast can save you about $10-15 easily. Buy croissant, juices and milk from outside and make your own tea/coffee in the room. If breakfast is included in your room rent, make sure to avail it.
Search for off-the-beaten-path tracks: Places like Nepal or Taipei, or Botswana, or Sri Lanka, or even Tharparkar or Khairpur are almost never in our sought after travel destinations.
Make a day to day plan and stick to it. Also make provisions for your day to day budget and firmly stick to it. Remember there are always trade offs while you are doing anything, so choose the best as per your circumstances and resources.
Less is More: travelling is both educating and relaxing in nature. Instead of ticking several destinations/places from a list of must-see attractions, give yourself some time to enjoy the actual place, its ambiance, culture and over all feel. Rather than spending majority of the day commuting from one place to the other in a vehicle, unpack, and then repack in the morning to go some place else, stay at least 2 nights at a particular place.