If you need some Internet access in Madrid, and pronto, you got options.
A call shop
Call shops in Madrid, called locutorios, have Internet-connected computers at the ready (sometimes with Skype and webcams) but they also offer phone booths with reasonable long-distance rates. Internet time is usually sold in 15-minute or one-hour increments.
Madrid’s locutorios are mom and pop shops that can be found almost everywhere, but if you’re looking for a slicker Kinko’s-like version, head to a Workcenter location.
If you brought along your laptop, then simply head to one of Madrid’s many Wi-Fi spots. A popular local blog called Madrid Me Mata has created a good visual map of Wi-Fi spots in Madrid that you can consult (and add to if you wish).