Airbnb ias you may know is not strictly a hotel search engine, but a platform for holiday rentals of houses, apartments, flats and rooms (in principle of private individuals, although many small hotels also offer beds).
Booking is a classic among the classics and its app lives up to what you would expect from this brand: agile, efficient, simple, intuitive and enjoyable. In Spain we use it a lot an it allows you to get discount everytime that you book an accommodation.
TripAdvisor. What to say about it? It is one of the best known apps for the quantity and quality of its establishments that are shown according to a ranking created from the user ratings. Really useful if you want to compare prices and the quality of the place.
Couchsurfing his is probably the best known way. It is a social network, where you can find accommodation anywhere in the world for free. Sometimes you will sleep on a sofa, sometimes on a mattress on the floor and at other times you can have a room for yourself. It is a great experience that will help you, not only to sleep for free, but also to meet local people.
HotelsCombined is one of the best hotel metasearch engines. That means that your search results are combined with dozens of search engines (such as Booking) and increase the chances of finding a cheap hotel.