Probably the easiest cocktail to make at home would be one that requires either a coke or water in it and the common alcohol. It would be easy to make this drink because you most likely would have all of the ingredients at your house and they are easy to make without having to get something from the liquor or grocery store. Also, you may not have to use any tools to make the drink.
The easiest cocktail to make is probably the Vodka and water. Vodka is a common alcohol that is usually kept in someone bar cabinet. Also, everyone has water. They are easy to pour and stir. Also, a rum and coke may be easy too because many people have rum in their liquor cabinet and they would also have coke in their refrigerator. Very little measuring is needed.