Dubai’s Hostel is located not far from DXB’s Terminal 2. This location is on the opposite side of the airport from the main terminals 1 and 3 of DXB. Dubai’s new airport DWC is around 50km away towards Abu Dhabi. You can reach the hostel by public transportation from either airport as the hostel is short walking distance from the Green Line Metro stop of “Stadium”, exiting and then follow the train tracks in the same direction. You will see the hostel just off the main road on your left.
From DXB take the Red line Metro towards UAE Exchange, changing to the Green line at Union station towards Etisalat. “Stadium” is the 5th stop.
From DWC take bus F55 to IBN Battuta metro station, then Red line Metro towards Rashidiya, changing to the Green line at Union station towards Etisalat. “Stadium” is the 5th stop.
I prefer to use www.Booking.com for finding accommodation in the UAE (and many other locations) as they tend to have the lowest prices, offer good discounts and usually have some type of free cancellation policy. You only need to prepay for non-refundable bookings. You can also earn American Airline Miles with Booking.com by going through AA's eShopping site!
Remember to read the reviews of the cheaper hotels and be realistic of expectations. If the hotel says it’s basic accommodation then expect that; possibly no frills and without free bars of soap or shampoo... I’ve read some reviews that were kind of harsh and possibly not entirely deserved. If the reviews say dirty, excessively noisy or unclean, then stay away. There are literally TONS of choices for accommodation in Dubai and the UAE, with more being built everyday!
The UAE Hostel Association also has hostels in Sharjah and Fujairah as listed on their website.