People love to drink warga, a sweet green tea. In Bissau, Portuguese beer and wine are popular. In more remote areas, fermented cashew, apple, sugar cane and oil palm make strong home brews. Juices from relatively exotic fruits like calabash and mandiple (from the eponymously named shrub) are excellent.
Outside of Bissau, which has bars and restaurants, your best bet is to head to the market – you don't need to look hard for places selling the local-style brews.