There are several processions on Good Friday. They all follow different routes depending on where the churches are located, but most pass through the center of town (carrera San Jerónimo, Sol, Calle Mayor, Plaza Mayor, etc.), so if you head to the center you should be able to see several of them. On that day they start between 7 and 8 in the evening, but I don't know exactly what time they'll be walking through the center. You can see the official schedule and information at
Munimadrid if you click on "Semana Santa".