In order to attain or collect (quickest way) the physical health insurance card tarjeta sanitaria individual, you will need to go to your nearest Centro de Salud (you can find this on the link attached below) :
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​https://centrossanitarios.sanidadmadrid.org/CentrosDireccion/misCentroPorDireccion.aspx

You can make a "cita previa" by calling the telephone number of the center. They will tell you what documents you need to bring in.
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Typically, the documents include: a valid TIE (ID card/work permit), your social security number and a copy of your empadronamiento (registration) certificate, however, you should verify with your specific health center.
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Below, you can see some screenshots of an example that could help you.
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Image 1
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​Image 2
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