Japan seemed to have no long term plans for the United States itself. It wanted to build an empire in the Far East (china, Indochina etc) to secure farmland and raw resources to feed its industrialised economy.

However America would stand in their way of doing this so they knew they had to knock them out of the war quickly. Pearl Harbour was supposed to achieve a knock out play on the Pacific fleet (destroying its aircraft carriers and making the base unusable preventing them from interfering with Japanese plans. With no way to stop the Japanese, they'd hoped the US, like Hitler hoped with Britain after the fall of France would sue for peace. Really Japanese plans seemed much more logical/calculated than Hitler's grand schemes.

But there were main who privately doubted that the plan would work. Yamamoto said he could only guarantee victory for sixth months and like Hitler, Japan had purged all foreign speaking people from government and so completely misread America and its resolve to fight on.

A rather more specific question than has been previously addressed, but you might be interested in some previous threads both about the goals of the Pearl Harbor attack in specific or the larger goals that the Japanese high command hoped to achieve in the aftermath of a successful war:

• Was the attack on Pearl Harbour a gamble by the Japanese Empire, or did they truly believed such a attack would cripple the US to the point of not winning the war? - the first top level answer gives a good overview of Japanese strategy in the opening stages of the war and it spawns a large amount of discussion and analysis of Japanese strategy in the immediate pre-war and beyond that you might find interesting.
• What did the Japanese expect the reaction to Pearl Harbor to be? - This commenters thread uses the Japanese view on the pre-war tensions to explore why the Pearl Harbor attacks were a logical extension of the Empire's goals and attitudes.
• What was Japan's plan for all the territories it acquired if they won the war? - This is definitely besides the point since you appear to be more interested in how the Empire wanted to deal with the Americans, but it's a good synopsis of the colonial situation in the immediate pre-war and the plans for expansion in the event of a successful war.