Generally speaking, in order to get from Edinburgh to New York City, you are going to have to fly. If you have unlimited funds, type in your point of origin and your destination and pick the flight that appeals to you. Other than that, you are going to have to research your travel dates as well as which airport is cheaper to fly into.
Websites like Skyscanner will give you an idea of the cheapest month to travel, however booking through complete third-party sites like Expedia can mean a cheap flight with fees rivaling that of a first-class ticket. If you have a preferred airline, consider booking directly through them or at least reviewing their prices and flight availability.
This may also give you a better idea of the cost you are looking at. If you really don't feel like researching, consider a boat or swimming.