The Prado offers free access to the museum between 6pm and 8pm Monday to Saturday and between 5pm and 7pm on Sundays and holidays. This is a generous offer as most museums offer just one free access day per month. However, free access means lengthy lineups and even if you're one of the first people in line, you'll only get two hours with the collection. Temporary exhibitions are also not included. If you're able to take advantage of this offer and don't mind the tight schedule, go for it!
Another way to save money is by buying a Paseo del Arte Ticket for €29,60. This is a great money-saver if you intend to visit Madrid's three major art museums: Museo Thyssen-Bornemisza, Museo Nacional del Prado and Museo Reina Sofía. You must redeem the ticket at whichever museum you bought the ticket from. Eg, if you bought the ticket on the Prado's website, you have to go to the Prado first to collect the ticket. Then you can use it at the other two attractions. The ticket offers a saving of 20%.
Similarly, if you're spending a bit of time in Spain, it's worth buying an Annual Membership card for National Museums for €36,06. This card gets you into dozens of national museums all over Spain for free.For a full list of museums included, see here.