[1] The "sweet" in the Thai name (หวาน, wan means 'sweet') refers to the particular color green itself and not to the taste of the curry.
Green curry paste is traditionally made by pounding in a mortar green bird's eye chillies, shallots, garlic, galangal, lemongrass, kaffir lime peel, cilantro roots (coriander), cumin seeds, white peppercorns, shrimp paste and salt.
Once the curry paste is cooked, more coconut milk and the remaining ingredients are added, along with a pinch of palm sugar and fish sauce.
Finally, as garnishes, Thai basil, fresh kaffir lime leaves, sliced phrik chi faa (the common name means 'sky-pointing chilies', which refers to large mild chilies such as Cayenne pepper) are often used.
For a more robust green curry, such as with seafood, julienned krachai (fingerroot or Chinese keys), white turmeric, and holy basil can be used as garnishes.