If you are an EU citizen, retiring in Spain is easy. You only need to show a minimum income of around 600 euro/month, and you get free state health and medical care. All this you can arrange after arriving in Spain just with your EU passport.
If you are a non-EU citizen, like American, it gets much more complicated. You need to apply for a long-stay retirement visa (visa de jubilados) at the Spanish consulate in US, and it isn't something that is routinely issued. Every application has to satisfy Spanish requirements in every detail. You first need a proof of non-earned income, such as pension, which you are able to receive in Spain plus private medical insurance valid in Spain. You must show evidence of housing - either owned outright or sufficient funds to obtain a rental property. You need a medical certificate showing you are free from certain communicable diseases, mental illness and drug addiction. You may also need a police clearance, showing you are free of criminal convictions. All documents must be officially translated into Spanish. Often a face-to-face interview is required with a consular officer. Applications sometimes need to be referred to Madrid, adding to the delay. Don't expect to get a reply for several months after applying.
Once over this hurdle and you get your prized visa in your passport, you then have to deal with the painfully slow Spanish bureaucracy after arrival to obtain your residence papers, for which you require a pile of documents and a lot of patience - you may be lucky to get your residence card in a few days, but more likely several months. And while you wait you cannot open a bank account or register a car - though some people were successful just showing a receipt of application for residencia.
You say you'll have around 1000 euro a month in Spain. Whether that's enough to live on partly depends where you are going to be based. Forget big cities like Madrid and Barcelona, as rents are sky-high. Many retirees migrate to the southern coasts because of milder climate (but very hot in summer) and presence of expats (mainly British and Northern Europeans). Seville is sizzling in summer (often over 42C/110F) but mild in winter (40-50F). Cost of living is lower than Madrid or Barcelona, but higher than in villages. Explore Seville is a useful website, maintained by a US expat living in Seville.
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