Unlike cities like Barcelona, finding accommodations in Sevilla when you're on a tight budget isn't too difficult. The first step is to become aware of your options and the teminology to avoid any surprises or rip-offs.
The cheapest and most basic accommodations you may find are called "fonda," that you can pick out by the blue sign with a white F, followed by a "pensión," indicated by a blue sign with a white P. The next step up before reaching hotel status is a "hostal," indicated by an Hs. Don't be surprised if these accommodations do not have private bathrooms- often times you either share a bathroom with others or pay extra for a private one.
For any of these three options, you can expect a price range of between €15 and €30. The price range of "fondas" and "pensiones" don't usually change according to their location in the city, while hostel prices will typically be higher in the cultural and touristic center versus around the periphery.
"Hostales," like hotels, have their own rating system based on a scale of one to three stars. A three-star hostel is approximately on par with a one-star hotel in terms of cost. Keep that in mind, as sometimes a one-star hotel can be your best option in terms of both quality and price.
There is a plethora of budget accommodations located throughout El Centro and Santa Cruz, but don't count out Triana and La Macarena.