Whether or not you need a visa to visit Curaçao depends on your nationality. On this website you'll find a complete list of nationalities that don't need a visa.
There are some exceptions where people who would need a visa based on just their nationality, but can be exempt if they have – for example – a multiple-entry short stay visa for a Schengen country, or a residence permit from the US or Canada. You can read more about this here: www.netherlandsandyou.nl/travel-and-residence/caribbean-visas/do-i-need-a-visa-for-the-caribbean-parts-of-the-kingdom
Should you require a visa for Curaçao, you can apply for one at your nearest embassy or consulate of The Netherlands.