well it says on the site I poste it for foreigners (assuming you do not have legal residency yet) you can get it with a passport for UE residents and your permit of residency if not EU .you go to your health center nearest you in Madrid , and will give you the health card to those living legally there and with low resources or with coverage from another country.

As it is legalise stuff, it is better to go with the minimum of information and ask them directly to constitute your file and application. You will be given a file to complete and return and they will mail the card to your place of residency there.

If you tell me where you are at like barrio in Madrid I can tell you where is the nearest health office to do so .Hope it helps.