I've used the Annual Spanish Museum Pass/Annual Membership card for National Museums/Tarjeta anual de Museos Estatales, the 36 euro one year museum pass.
To explain the process, you can go to any of the museums that accept the annual museum pass and buy it at the ticket counter. My personal advice, buy the annual pass at a less popular museum so you're not holding up a long line with the small amount of paperwork needed. I bought mine at the Museo del Romanticismo. They just need a photo ID from you, I used my American driver's license and they wrote my driver's license ID on the Museum Pass as the ID number. I think your passport would be the preferred form of ID, but apparently you can just use any government photo ID.
Once you have your Annual Museum Pass, you just present the pass and your ID at the main ticket office of the museum and they give you a ticket. Smaller museums may not even care to see your ID, or even care if you pay the entry fee, I've been waived through at some Madrid museums because the person working the desk was busy with something else. The smaller museums can be pretty empty and they don't seem very fussed about the formalities or getting 3 euros from every patron.
For the Prado specifically, here's what I've done. Go to the ticket office on the north exterior of the museum (Goya statue side), give them my annual pass and ID, and I get a ticket, and it's a quick walk to the Jerónimos entrance. When I did this at opening (10am) on a Sunday, I was in a practically empty Prado with barely any waiting. Obviously, the ticket line can get long at peak times so beware of that. Other days, I've waited 10-15 minutes to get my ticket, even near the opening time in the morning.
And, since you want to see the Prado multiple times, I would just get the Annual Pass.
A few other notes:
- The Sorolla Museum is closed until early 2026.
- The Archaeological Museum is actually really good.
- Museo de America is nicely paired with visiting the Faro de Moncloa observation deck for a nice view of the city.
- National Museum of Anthropology is pretty skippable.
- Get to the Reina Sofia when it opens, and head straight for Guernica, (your ticket gets checked twice so keep it handy, FYI) so you can see it without any crowds.