There’s not much in the way of budget accommodation in Dubai. Cheap guest house style accommodation that is common in Asian destinations does not fit in with Dubai’s grandmaster plan of being a luxury holiday and shopping stop-over hub.
There is one hostel in Dubai, the UAE YHA, though it’s not in the most convenient location.
There are budget accommodation options available, but booking online is generally not possible. Most of these places don’t even have a website, let alone booking facilities, and their contact details are via a yahoo address.
If you are looking for a guest house in Dubai they can be found in the Deira and Bur Dubai area (the Dubai Creek area). I found a number of places that had single room accommodation for 150 UAE Dirham (about $40 US) .
These guest houses are spread out all over the city as well, so it’s not like you can turn up in an area and look around, like in Khao Sanh Road in Bangkok or Colaba in Mumbai.
[Mirage Guest House, an example of a basic Dubai guest house.]
To find a cheap hotel in Dubai try HotelsCombined which compares multiple hotel booking websites at once.
More links on Dubai travel can be found in the Dubai Travel Guide.