Some people think it’s disgusting to eat snails, but I love it!
Snail season starts in May and goes till August, so during this period, visit a restaurant or snack bar that serves snails, order a beer (or "imperial" as we call it), and be sure to get bread for dipping in the sauce. (Usually the sauce contains olive oil and oregano, among other ingredients.)
One of the best places to dine on snails is “O Filho do Menino Júlio dos Caracóis” on Vale Formoso de Cima Street. It doesn’t have a terrace, and it's not in a touristy area. You can take bus 749 (Campo Pequeno) or 794 (Oriente Station) or simply take a taxi.
You can find snails in Lisbon's center, too—in restaurants and snack bars. Just look for a snail drawing in the window.