At the time Hitler declared war on the U.S. there was no existing plan for how to win it at all.
In fact, based on all the information I have studied, I have come to the opinion that the timing of the whole thing was more about the German military situation in Russia at that moment. I really don't think Hitler had any plans of a serious German war effort against the U.S. ever. Or at least not before England was dealt with. Something that was still a year or two away.
The following supports this opinion:
Short of saying it in a speech, Germany couldn't DO anything that would make a real war difference against America. Hitler did lift the ban he had on German U-boats attacking U.S. shipping but they were still looking more to enforce a naval blockade against England or sinking Russian shipments.
What is the point in giving America justification to join England in any overt actions against his Reich at that time? The answer is there is no point. Making dumb moves like that fits the Hitler of the comming desperation times but not of late 1941. The Hitler of 1941 still worked situations to his benefit in most cases.
It was during the very week of the Japanese attack on Pearl Harbor, operation Barbarosa ground to a halt at the gates of Moscow. Right after the stall (December 5th and 6th, 1941), the Soviets attacked German forces around Moscow with forces that included 70 fresh divisions of well equipped, Siberian troops. Troops that the German High Command didn't think were available.
From the 5th on, the Soviets began a counter-offensive and were making small gains (a mile or less) in several areas. On the 6th, Soviet Thitieth Army broke into Third Panzer Group's left flank northeast of Klin to a distance of eight miles, almost creating a complete breakthrough.
German generals were reporting all along the line about the fresh, well trained and equipped Russian Siberian forces. For the next several days German forces were retreating west from Moscow.
Early on, it looked at times like the routs the German were accustomed to creating but they were the ones on the run. On the 10th of December, Guderian characterized his Second Panzer Army as a scattered assemblage of armed baggage trains slowly wending their way to the rear.
Hitler knew very well everything that was happening along the front. He was updated several times a day. He knew his armies were stalled and falling back. He also knew that unless something changed quickly, the Moscow objective could not be accomplished in 1941.
Though its certain he was shocked as this type situation had never occurred up until this time. Still, Hitler was not at a point where he was delusional and making up defensive formations yet. He knew Germany had a real issue here and likely thought he could work their way out of it.
In addition, Hitler was aware that his nation's strategic fuel reserves were low and some of the German armies in Russia were well short of normal strength. He had plans for how to get troop strengths back up but the oil situation alone threatened everything.
In order to turn the situation immediately, Hitler was looking for ways to change things on the Russian front. It is my opinion he hoped declaring war on the U.S. would induce Japan to reciprocate the gesture by declaring war on the Soviets. Or at the least, he hoped to persuade his ally to create concerns along the Russian border.
The Soviets and Japanese were not allys by any stretch. Rather, they were old enemies. In fact, Stalin had feared a Japanese attack on the Russian Eastern border since the war bagan. It was very reluctantly--and possibly out of desperation--that he had moved forces from there to the Moscow area. Even then it was only after Stalin's senior Japanese spy convinced him that Japan was looking East, not West.
If successful in influencing Stalin to pull some of these forces back, Hitler was still under the mistaken impression the Russians were completely out of reserves. He felt that victory was that close. If he could get the situation back to where it was just before the deep freeze began, they could resume the attack--and quickly win Moscow.
Other than his hopes for immediate help with the Soviet situation--which would have been admitted to NO ONE by the Nazi regime--it is unexplainable that Hitler would just up and declare war on America without substancial upside for his country at the time.