TL;DR: It’s tough to find info on getting to the Recife stadium for the World Cup. If you’re a do-it-yourself kind of person, you won’t take a taxi but will opt for the metro+bus or metro+taxi. Go to the second to last station called Cosme e Damião (here’s the metro map) then get a bus or a taxi to the stadium (Arena Pernambuco). If you do opt for the taxi only route, it’s 30 min. without traffic (good luck) or 1 hour with moderate traffic.
This image came up on my Twitter feed. It’s from Pernambuco.com and shows the distances between metro stations and sporting arenas in different cities. Obviously, the Recife example is the worst in terms of distance. It led me to wonder about what the metro station is called, what is near the metro station and how far it all is from downtown Recife.
Google Maps requires you to enter “Arena Pernambuco, São Lourenço da Mata” to find the stadium, that’s because it’s actually in a different city about 20km from downtown Recife (though considered part of the greater Recife area). Upon clicking the map, I zoomed in to see what little blue metro marker showed up as closest metro station to the arena. The only result was the Camaragibe station (the last station on the red line). What it didn’t show was the actual metro station referenced in the image above (the one that’s 4.1km from the arena), which is called Cosme e Damião station (the stop before Camaragibe). I had to ask for directions to there from Google Maps in order to get a basic visualization of the logistics. Below is a map I found online showing the distance from Recife and, below that, an image from the stadium’s official site (PT) where you can better see the area (click to enlarge). Here’s two other images (via a small PDF), though with info in Portuguese, that might help you with logistics.