A few good sites we used to get a house:
fotocasa.es
pisos.com
idealista.com
The sites allow to filter for house rentals, just make sure you only select residential rentals, not those with rentals with a purchase option or vacation rentals. Sometimes owners will try to hide that they are actually posting vacation rentals, so it requires reading listing in detail.
Also take into account that there are two kinds of listings, those by agencies and those by private persons. Agencies will charge a month rental for their mediation, so directly dealing with owners saves some money, but one often doe snot get the best properties that way.
Also take into account that agencies will require proof of income and sometimes other papers like a bank guarantee.
Make sure that you are well prepared, so first get registered with the local Policia Nacional as a foreigner with and NIE number (show your passport).
With that registration number and proof of income (English version is often enough) you need to open a bank account.
That bank account will allow you to pay your landlord as well as utilities.
Upon receiving a signed rental agreement use it and the NIE number to get registered with your town or city.
If possible, let the owner do the payments of utilities if they are already in his name. Quite common in Spain.
Take into account that most landlords have not thought well about renting out their property, so put something on repairs and maintenance in the contract.
Rental prices are negotiable most of the times.
Take into account that realty is not a regulated profession, so anyone can become a realtor here and 99% of realtors are terrible at it. Most of them do not respond to emails or messages or voice mails, so make sure to call instead. Also make sure to call during office hours, so not during siestas or weekends or one of many holidays. They are often also notoriously resistant at working beyond office hours.
Take into account that the owner of a house may often be present when you visit the property offered by the realtor, which also makes it harder to make an appointment for viewing.
Do not be surprised if some owners say outright that they do not rent to foreigners. Do not take it personally. Their loss.
Always ask about heating and airconditioning systems in the house, not just what systems but also about their last maintenance and age. There is lot of old junk out there. Beware also of electrical heating as electricity is very costly here. Wood brickets are cheapest, followed by diesel oil.
Take into account that getting a phone connection is a pain and can take weeks if not months. Best is to get a prepaid SIM right away at a cell phone store for 9,99 (have to show a passport). One needs a phone to communicate with one's realtors, home owners vendors here.
Speaking Spanish puts you way ahead of course, otherwise you will get overcharged more often than not. English skills are too often very poor all over the country.
To go look at houses, if you have no car yet, consider renting with a local small car rental, not the big ones. Saves tons of money, often 50%. Avoid renting big cars. The roads, garages and parkings often limit you to using smaller cars.
Single family houses in big cities are usually very costly, so one needs to go look outside those then in the many little town surrounding them. Saves a ton of money and availability is plenty.